// Numbas version: finer_feedback_settings
{"question_groups": [{"name": "Group", "pickQuestions": 1, "pickingStrategy": "all-shuffled", "questions": [{"name": "Numerical reasoning - average salary", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "functions": {"commanumber": {"definition": "var parts=n.toString().split(\".\");\n        if(parts[1] && parts[1].length<2) {\n      parts[1]+='0';\n        }\n        return parts[0].replace(/\\B(?=(\\d{3})+(?!\\d))/g, \",\") + (parts[1] ? \".\" + parts[1] : \"\");", "type": "string", "language": "javascript", "parameters": [["n", "number"]]}}, "tags": ["average", "maths-aid", "mean", "money", "numerical reasoning", "percentage", "weighted"], "advice": "<p>This is a weighted average.</p>\n    <p>The average value is given by multiplying each salary value by the frequency with which it occurs amongst the staff (in fraction form), and adding the resulting numbers together.</p>\n    <p>For example, the salary &pound;{commanumber(salary[0])} has a frequency of {per[0]}% which is $\\frac{\\var{per[0]}}{100} = \\var{per[0]/100}$. When we multiply these together we get \\[ &pound;\\var{latex(commanumber(salary[0]))} \\times \\frac{\\var{per[0]}}{100} = \\var{salary[0]*per[0]/100}. \\]</p>\n    <p>For this question we have 4 salary values and the weighted average is \\[\\begin{align} &amp; \\frac{\\var{per[0]}}{100} \\times \\var{latex(commanumber(salary[0]))} + \\frac{\\var{per[1]}}{100} \\times \\var{latex(commanumber(salary[1]))} + \\frac{\\var{per[2]}}{100} \\times \\var{latex(commanumber(salary[2]))} + \\frac{\\var{per[3]}}{100} \\times \\var{latex(commanumber(salary[3]))} \\\\ &amp;= &pound;\\var{latex(commanumber(salary[0]*per[0]/100))} +&nbsp;&pound;\\var{latex(commanumber(salary[1]*per[1]/100))} + &pound;\\var{latex(commanumber(salary[2]*per[2]/100))} + &pound;\\var{latex(commanumber(salary[3]*per[3]/100))} \\\\ &amp;= &pound;\\var{latex(commanumber(average))} \\end{align} \\]</p>", "rulesets": {}, "parts": [{"prompt": "<p>What is the average salary?</p>\n        <p>&pound; [[0]]</p>", "gaps": [{"minvalue": "average", "type": "numberentry", "maxvalue": "average", "marks": 1.0, "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}], "statement": "<p>In a department {per[0]}% of the staff have a salary of &pound;{commanumber(salary[0])}, {per[1]}% a salary of &pound;{commanumber(salary[1])}, {per[2]}% a salary of &pound;{commanumber(salary[2])}, and {per[3]}% a salary of &pound;{commanumber(salary[3])}.</p>", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"salary": {"definition": "shuffle([salary0,salary1,salary2,salary3])", "name": "salary"}, "salary1": {"definition": "random(15000..50000#5000 except salary0)", "name": "salary1"}, "salary0": {"definition": "random(15000..50000#5000)", "name": "salary0"}, "salary3": {"definition": "random(15000..50000#5000 except [salary0,salary1,salary2])", "name": "salary3"}, "salary2": {"definition": "random(15000..50000#5000 except [salary0,salary1])", "name": "salary2"}, "average": {"definition": "(per[0]*salary[0]+per[1]*salary[1]+per[2]*salary[2]+per[3]*salary[3])/100", "name": "average"}, "per": {"definition": "shuffle([per0,per1,per2,per3])", "name": "per"}, "per3": {"definition": "100-per0-per1-per2", "name": "per3"}, "per2": {"definition": "random(10..min(50,90-per0-per1)#10)", "name": "per2"}, "per1": {"definition": "random(10..min(50,80-per0)#10)", "name": "per1"}, "per0": {"definition": "random(10..50#10)", "name": "per0"}}, "metadata": {"notes": "", "description": "<p>Compute the weighted average salary in a department, given four salary levels and the percentages of staff earning them.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Numerical reasoning - lottery syndicate", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["lottery", "maths-aid", "money", "numerical reasoning", "ratio", "shares"], "metadata": {"description": "<p>Given the stakes of three people in a lottery syndicate, and the amount the syndicate won, work out each person's share of the winnings.</p>\n                    <p>Based on question 4 from section 3.2 of the Maths-Aid workbook on numerical reasoning.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>{names[0]}, {names[1]} and {names[2]} agree to buy {numbernames[total]} pounds' worth of lottery tickets, with {names[0]} contributing &pound;{share[0]}, {names[1]} contributing &pound;{share[1]} and {names[2]} contributing &pound;{share[2]}.</p>\n<p>They agree that if they win anything with any of these tickets that it should be shared out in the same ratio as their contributions.</p>", "advice": "<p>Their agreement means that the winnings should go to {names[0]}, {names[1]} and {names[2]} in the ratio $\\var{share[0]}:\\var{share[1]}:\\var{share[2]}$. Think of these as being shares in the winnings.</p>\n<p>There are $\\var{share[0]}+\\var{share[1]}+\\var{share[2]} = \\var{total}$ shares in all for the &pound;{win}.</p>\n<p>Hence each share is worth $&pound;\\var{win} \\div \\var{total} = &pound;\\var{part}$.</p>\n<p>So {names[0]} gets {share[0]} {pluralise(share[0],'share','shares')} = $\\var{share[0]} \\times &pound;\\var{part} = &pound;\\var{winnings[0]}$, {names[1]} {share[1]} {pluralise(share[1],'share','shares')} = $\\var{share[1]} \\times &pound;\\var{part} = &pound;\\var{winnings[1]}$ and {names[2]} {share[2]} {pluralise(share[2],'share','shares')} = $\\var{share[2]} \\times &pound;\\var{part} = &pound;\\var{winnings[2]}$.</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"numbernames": {"name": "numbernames", "group": "Ungrouped variables", "definition": "['zero','one','two','three','four','five','six','seven','eight','nine','ten','eleven','twelve','thirteen','fourteen','fifteen','sixteen','seventeen','eighteen','nineteen']", "description": "", "templateType": "anything", "can_override": false}, "winnings": {"name": "winnings", "group": "Ungrouped variables", "definition": "map(x*part,x,share)", "description": "", "templateType": "anything", "can_override": false}, "names": {"name": "names", "group": "Ungrouped variables", "definition": "shuffle(['Bob','Terry','Cilla','Jim','Margaret','Cyril','Ethel','Horace','Beryl'])[0..3]", "description": "", "templateType": "anything", "can_override": false}, "share": {"name": "share", "group": "Ungrouped variables", "definition": "shuffle([share0,share1,share2])", "description": "", "templateType": "anything", "can_override": false}, "share1": {"name": "share1", "group": "Ungrouped variables", "definition": "random(1..min(floor(total/2),total-1-share0))", "description": "", "templateType": "anything", "can_override": false}, "share0": {"name": "share0", "group": "Ungrouped variables", "definition": "random(1..floor(total/2))", "description": "", "templateType": "anything", "can_override": false}, "share2": {"name": "share2", "group": "Ungrouped variables", "definition": "total-share0-share1", "description": "", "templateType": "anything", "can_override": false}, "part": {"name": "part", "group": "Ungrouped variables", "definition": "win/total", "description": "", "templateType": "anything", "can_override": false}, "win": {"name": "win", "group": "Ungrouped variables", "definition": "random(2..10)*total*5", "description": "", "templateType": "anything", "can_override": false}, "total": {"name": "total", "group": "Ungrouped variables", "definition": "random(6..15)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["numbernames", "winnings", "names", "share", "share0", "share1", "share2", "part", "win", "total"], "variable_groups": [], "functions": {"pluralise": {"parameters": [["n", "number"], ["single", "string"], ["plural", "string"]], "type": "string", "language": "javascript", "definition": "return Numbas.util.pluralise(n,single,plural);"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>They win &pound;{win}. How much does each get?</p>\n<table>\n<tbody>\n<tr>\n<td>{names[0]}</td>\n<td>&pound; [[0]]</td>\n</tr>\n<tr>\n<td>{names[1]}</td>\n<td>&pound; [[1]]</td>\n</tr>\n<tr>\n<td>{names[2]}</td>\n<td>&pound; [[2]]</td>\n</tr>\n</tbody>\n</table>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "winnings[0]", "maxValue": "winnings[0]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "winnings[1]", "maxValue": "winnings[1]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}, {"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "winnings[2]", "maxValue": "winnings[2]", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Numerical reasoning - price markup", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "functions": {}, "tags": ["maths-aid", "money", "numerical reasoning", "percentage", "price", "profit"], "advice": "<p>In order to realise a profit of {profit}%, the selling price of the item must be {100+profit}% of the cost of production.</p>\n  <p>This price is $\\frac{\\var{100+profit}}{100} \\times \\var{produce} = &pound;\\var{sell}.$</p>\n  <p>When rounding this to the nearest penny, a decision has to be made whether the price is &pound;{floor(sell*100)/100} or &pound;{ceil(sell*100)/100}. Usually,&nbsp;if the&nbsp;next digit after the one being rounded is&nbsp;{if(fract(sell*100)&lt;0.5,'less than 5 then we round down','greater than or equal to 5 then we round up')}, so we take the price to be <strong>&pound;{dpformat(sell,2)}</strong>.</p>", "rulesets": {}, "parts": [{"prompt": "<p>Give your answer to the nearest penny.</p>\n      <p>&pound; [[0]]</p>", "gaps": [{"precisiontype": "dp", "precisionmessage": "<p>You didn't give your answer to the nearest penny. Round your answer to two decimal places.</p>", "maxvalue": "precround(sell,2)+0.005", "minvalue": "precround(sell,2)-0.005", "precisionpartialcredit": 50.0, "precision": 2.0, "marks": 1.0, "type": "numberentry", "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}], "statement": "<p>An item costs <strong>&pound;{dpformat(produce,2)}&nbsp;</strong>to produce. How much should the manufacturer sell these items for if it wants to realise a profit of&nbsp;<strong>{profit}%</strong>&nbsp;on these items?</p>", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"profit": {"definition": "random(5..35#10)", "name": "profit"}, "sell": {"definition": "produce*(1+profit/100)", "name": "sell"}, "produce": {"definition": "random(2..10)+random(0.25,0.75,0.50)", "name": "produce"}}, "metadata": {"notes": "", "description": "<p>Given the cost to produce an item and a desired markup, calculate the appropriate sale price.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Numerical reasoning - tax", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}], "tags": ["income", "money", "numerical reasoning", "percentage", "Percentage", "tax"], "metadata": {"description": "<p>Given an annual salary, tax allowance, tax rate and pension deduction, work out a person's take-home pay per month.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>{names} has a salary of <strong>&pound;{commanumber(salary)}</strong> per year.</p>\n<p>{capitalise(he)} has a tax allowance of <strong>&pound;{commanumber(allowance)}</strong> and {he} pays income tax at <strong>{tax}%</strong> on the rest.</p>\n<p>{capitalise(he)} pays into a pension and for this {his} salary is deducted <strong>{pension}%</strong> after tax has been deducted.</p>", "advice": "<p>{names} is only taxed on the amount remaining after taking away the allowance, i.e. $&pound;\\var{commanumber(salary)} - &pound;\\var{commanumber(allowance)} = &pound;\\var{commanumber(salary-allowance)}.$</p>\n<p>Income tax is {tax}% on this $&pound;\\var{commanumber(salary-allowance)}$ and is $&pound;\\var{latex(commanumber(salary-allowance))} \\times \\frac{\\var{tax}}{100} &nbsp;= &pound;\\var{commanumber(taxedincome)}.$</p>\n<p>This leaves {names} with $&pound;\\var{commanumber(salary)} - &pound;\\var{commanumber(taxedincome)} = &pound;\\var{commanumber(aftertax)}.$</p>\n<p>{pension}% of this is for {his} pension contributions, i.e. $&pound;\\var{commanumber(aftertax)} \\times \\frac{\\var{pension}}{100} = &pound;\\var{commanumber(pensiondeduction)}.$</p>\n<p>The amount left is then $&pound;\\var{commanumber(aftertax)} - &pound;\\var{commanumber(pensiondeduction)} = &pound;\\var{commanumber(precround(netincome,2))}.$</p>\n<p>The take home pay per month is hence $\\frac{\\var{netincome}}{12} = &pound;\\var{commanumber(incomepermonth)}$, to the nearest penny.</p>", "rulesets": {}, "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"salary": {"name": "salary", "group": "Ungrouped variables", "definition": "random(18000..50000#1000)", "description": "", "templateType": "anything", "can_override": false}, "aftertax": {"name": "aftertax", "group": "Ungrouped variables", "definition": "salary-taxedincome", "description": "", "templateType": "anything", "can_override": false}, "incomepermonth": {"name": "incomepermonth", "group": "Ungrouped variables", "definition": "precround(netincome/12,2)", "description": "", "templateType": "anything", "can_override": false}, "his": {"name": "his", "group": "Ungrouped variables", "definition": "if(he='he','his','her')", "description": "", "templateType": "anything", "can_override": false}, "names": {"name": "names", "group": "Ungrouped variables", "definition": "if(he='he',random(['Bob','Bill','Ben','Barry']),random(['Bridget','Beth','Bea','Beatrice']))", "description": "", "templateType": "anything", "can_override": false}, "netincome": {"name": "netincome", "group": "Ungrouped variables", "definition": "(allowance+(salary-allowance)*(1-tax/100))*(1-pension/100)", "description": "", "templateType": "anything", "can_override": false}, "pensiondeduction": {"name": "pensiondeduction", "group": "Ungrouped variables", "definition": "aftertax*pension/100", "description": "", "templateType": "anything", "can_override": false}, "tax": {"name": "tax", "group": "Ungrouped variables", "definition": "random(15..30)", "description": "", "templateType": "anything", "can_override": false}, "pension": {"name": "pension", "group": "Ungrouped variables", "definition": "random(3..15)", "description": "", "templateType": "anything", "can_override": false}, "taxedincome": {"name": "taxedincome", "group": "Ungrouped variables", "definition": "(salary-allowance)*tax/100", "description": "", "templateType": "anything", "can_override": false}, "allowance": {"name": "allowance", "group": "Ungrouped variables", "definition": "random(1000..10000#1000)", "description": "", "templateType": "anything", "can_override": false}, "he": {"name": "he", "group": "Ungrouped variables", "definition": "random('he','she')", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["salary", "aftertax", "incomepermonth", "his", "names", "netincome", "pensiondeduction", "tax", "pension", "taxedincome", "he", "allowance"], "variable_groups": [], "functions": {"commanumber": {"parameters": [["n", "number"]], "type": "string", "language": "javascript", "definition": "var parts=n.toString().split(\".\");\n        if(parts[1] && parts[1].length<2) {\n      parts[1]+='0';\n        }\n        return parts[0].replace(/\\B(?=(\\d{3})+(?!\\d))/g, \",\") + (parts[1] ? \".\" + parts[1] : \"\");"}}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "<p>How much does {he} get per month, assuming that these are the only deductions?</p>\n<p>&pound; [[0]] (to the nearest penny)</p>", "gaps": [{"type": "numberentry", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "minValue": "incomepermonth", "maxValue": "incomepermonth", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "precisionType": "dp", "precision": 2, "precisionPartialCredit": 100, "precisionMessage": "", "strictPrecision": true, "showPrecisionHint": false, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "sortAnswers": false}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "type": "question"}, {"name": "Partial sum of an arithmetic sequence - birthday money", "extensions": ["random_person"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Hannah Aldous", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1594/"}], "variable_groups": [{"variables": ["person", "pronouns"], "name": "A person"}], "functions": {}, "rulesets": {}, "ungrouped_variables": ["m", "n", "c", "ci", "ni", "b", "first"], "metadata": {"description": "<p>The amount of money a person gets on their birthday&nbsp;follows an arithmetic sequence.</p>\n<p>Calculate the amount&nbsp;on a given birthday, then calculate the sum up to that point.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "advice": "<p>We are told that {person['name']}'s parents&nbsp;deposit a uniformly&nbsp;increasing&nbsp;amount of money into&nbsp;a savings account&nbsp;for {person['name']} every&nbsp;year on&nbsp;{person['name']}'s&nbsp;birthday.</p>\n<p>We are&nbsp;also given the amount of money that&nbsp;{person['pronouns']['their']} parents deposit into the account&nbsp;on&nbsp;{person['pronouns']['their']} first $3$ birthdays:</p>\n<ul>\n<li>On {person['pronouns']['their']}&nbsp;$1^{st}$ birthday, they deposited $&pound;\\var{first}$ into the account.</li>\n<li>On {person['pronouns']['their']}&nbsp;$2^{nd}$ birthday, they deposited $&pound;\\var{b[1]+first}$ into the account.</li>\n<li>On {person['pronouns']['their']}&nbsp;$3^{rd}$ birthday, they deposited $&pound;\\var{b[1]*2+first}$ into the account.</li>\n</ul>\n<h4>a)</h4>\n<p>To calculate the&nbsp;amount of money&nbsp;{person['name']}'s parents&nbsp;would deposit&nbsp;into the savings account on&nbsp;{person['pronouns']['their']} 21<sup>st</sup>&nbsp;birthday, if {pronouns['their']} parents maintained this pattern, we&nbsp;use the equation</p>\n<p>\\[a_n=a_1+(n-1)d\\text{,}\\]</p>\n<p>where</p>\n<ul>\n<li>$a_1$ is the first&nbsp;term;</li>\n<li>$a_n$ is the $n^{\\text{th}}$ term;</li>\n<li>$d$ is the common difference between consecutive terms.</li>\n</ul>\n<p>To identify the first term and common difference of the sequence we can use a table like the one below.</p>\n<table border=\"1\">\n<thead></thead>\n<tbody>\n<tr>\n<th>$n$</th>\n<td>$1$</td>\n<td>$2$</td>\n<td>$3$</td>\n</tr>\n<tr>\n<th>$a_n$</th>\n<td>$\\mathbf{\\var{first}}$</td>\n<td>$\\var{b[1]+first}$</td>\n<td>$\\var{b[1]*2+first}$</td>\n</tr>\n<tr>\n<th>First differences</th>\n<td></td>\n<td>$\\mathbf{\\var{b[1]}}$</td>\n<td>$\\mathbf{\\var{b[1]}}$</td>\n</tr>\n</tbody>\n</table>\n<p>The first term&nbsp;and common difference have been highlighted in bold: $a_1 = \\var{first}$ and $d = \\var{b[1]}$.</p>\n<p>Now we&nbsp;can use these to calculate $a_{21}$, giving us</p>\n<p>\\begin{align}<br/>a_{21}&amp;=\\var{first}+\\var{b[1]} \\times (21-1) \\\\<br/>&amp;=\\var{first+b[1]*(20)}\\text{.} \\\\<br/>\\end{align}</p>\n<p>So, assuming that {person['name']}'s parents do maintain this pattern, on {pronouns['their']}&nbsp;21<sup>st</sup>&nbsp;birthday {pronouns['their']} parents will&nbsp;deposit $&pound;\\var{first+b[1]*(20)}$ into the savings account.</p>\n<h4>b)</h4>\n<p>We are now asked to calculate&nbsp;the total&nbsp;amount of&nbsp;money that {person['name']}'s&nbsp;parents will&nbsp;have added to this savings account over 21 years, including the money that&nbsp;{pronouns['their']} parents will&nbsp;deposit into the account on {pronouns['their']} 21<sup>st</sup>&nbsp;birthday.</p>\n<p>This question involves calculating the sum using the equation</p>\n<p>\\[\\sum\\limits_{i=1}^n{a_i}=\\frac{n}{2}(a_1+a_n)\\text{.}\\]</p>\n<p>We know from part <strong>a) </strong>that</p>\n<p>\\begin{align}<br/>a_1&amp;=\\var{first},\\\\<br/>n&amp;=21,\\\\<br/>a_{21}&amp;= \\var{first+b[1]*(20)}.<br/>\\end{align}</p>\n<p>Using&nbsp;our formula for the sum,</p>\n<p>\\begin{align}<br/>\\sum\\limits_{i=1}^n{a_i}&amp;=\\frac{n}{2}(a_1+a_n)\\\\<br/>&amp;=\\frac{\\var{21}}{2}(\\var{first}+\\var{first+b[1]*(21-1)})\\\\<br/>&amp;=\\var{21*(first+first+b[1]*(20))/2}\\text{.}<br/>\\end{align}</p>\n<p>Therefore, over 21 years {person['name']}'s&nbsp;parents will&nbsp;have added a total of $&pound;\\var{21*(first+first+b[1]*(20))/2}$&nbsp;to this savings account!</p>", "statement": "<p>{person['name']}'s parents&nbsp;deposit a uniformly&nbsp;increasing&nbsp;amount of money into&nbsp;a savings account&nbsp;for {pronouns['them']} every&nbsp;year on {pronouns['their']}&nbsp;birthday:</p>\n<ul>\n<li>on&nbsp;{pronouns['their']} first&nbsp;birthday&nbsp;{pronouns['their']} parents deposited&nbsp;$&pound;\\var{first}$ into the account;</li>\n<li>on&nbsp;{pronouns['their']} second&nbsp;birthday&nbsp;{person['pronouns']['their']} parents&nbsp;deposited&nbsp;$&pound;\\var{b[1]+first}$ into the account;</li>\n<li>on {pronouns['their']} third&nbsp;birthday&nbsp;{pronouns['their']} parents&nbsp;deposited $&pound;\\var{b[1]*2+first}$ into the account.</li>\n</ul>\n<p>{person['name']} wants to know&nbsp;the total amount&nbsp;of&nbsp;money&nbsp;that will be in&nbsp;this savings account,&nbsp;excluding interest,&nbsp;after&nbsp;{pronouns['their']} 21<sup>st</sup>&nbsp;birthday, if&nbsp;{pronouns['their']} parents maintain this pattern.</p>", "preamble": {"js": "", "css": ""}, "variables": {"c": {"name": "c", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "repeat(random(3..13 except[10]),8)"}, "n": {"name": "n", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "repeat(random(3..9),7)"}, "person": {"name": "person", "description": "<p>A random person</p>", "templateType": "anything", "group": "A person", "definition": "random_person()"}, "m": {"name": "m", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "repeat(random(2..10),5)"}, "first": {"name": "first", "description": "<p>first term in the sequence</p>", "templateType": "anything", "group": "Ungrouped variables", "definition": "random(10..15 #5)"}, "pronouns": {"name": "pronouns", "description": "", "templateType": "anything", "group": "A person", "definition": "person['pronouns']"}, "ni": {"name": "ni", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "repeat(random(19..40),10)"}, "b": {"name": "b", "description": "<p>a</p>", "templateType": "anything", "group": "Ungrouped variables", "definition": "repeat(random(10..25 #5), 3)"}, "ci": {"name": "ci", "description": "", "templateType": "anything", "group": "Ungrouped variables", "definition": "repeat(random(6..20),10)"}}, "parts": [{"variableReplacementStrategy": "originalfirst", "prompt": "<p>How much money will&nbsp;{person['name']}'s parents deposit&nbsp;into the savings account on {pronouns['their']} 21<sup>st</sup>&nbsp;birthday,&nbsp;if {pronouns['their']} parents maintain this pattern?&nbsp;</p>\n<p>&pound;[[0]].</p>", "stepsPenalty": 0, "gaps": [{"answer": "{first+b[1]*(20)}", "showpreview": true, "expectedvariablenames": [], "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "checkingtype": "absdiff", "type": "jme", "checkingaccuracy": 0.001, "variableReplacements": [], "vsetrange": [0, 1], "checkvariablenames": false, "showFeedbackIcon": true, "scripts": {}, "marks": 1, "showCorrectAnswer": true}], "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "gapfill", "marks": 0, "steps": [{"variableReplacementStrategy": "originalfirst", "prompt": "<p>Use the arithmetic formula,</p>\n<p>\\[a_n = a_1 + (n-1)d, \\]</p>\n<p>where</p>\n<ul>\n<li>$a_n$ is the $n^\\text{th}$ term;</li>\n<li>$a_1$ is the first&nbsp;term in&nbsp;the sequence;</li>\n<li>$d$ is the common difference between consecutive terms.</li>\n</ul>", "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "information", "marks": 0, "showCorrectAnswer": true}, {"variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "maxValue": "{first}", "allowFractions": false, "prompt": "<p>What is the value of $a_1$?</p>", "mustBeReducedPC": 0, "minValue": "{first}", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": "0.2", "scripts": {}}, {"variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "maxValue": "{b[1]}", "allowFractions": false, "prompt": "<p>What is the value of $d$?</p>", "mustBeReducedPC": 0, "minValue": "{b[1]}", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": "0.2", "scripts": {}}, {"variableReplacementStrategy": "originalfirst", "prompt": "<p>Now use the formula to calculate&nbsp;$a_{21}$.</p>", "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "information", "marks": 0, "showCorrectAnswer": true}], "showCorrectAnswer": true}, {"variableReplacementStrategy": "originalfirst", "prompt": "<p>How much money will&nbsp;{person['name']}'s&nbsp;parents have added to this savings account over&nbsp;$21$ years in total, including the money that&nbsp;{person['pronouns']['their']} parents will&nbsp;deposit into the account on {person['pronouns']['their']} $21^{st}$ birthday?</p>\n<p>&pound;[[0]].</p>\n<p></p>", "stepsPenalty": 0, "gaps": [{"variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "type": "numberentry", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "maxValue": "{21*(first+first+b[1]*(20))/2}", "allowFractions": false, "mustBeReducedPC": 0, "minValue": "{21*(first+first+b[1]*(20))/2}", "mustBeReduced": false, "variableReplacements": [], "showFeedbackIcon": true, "showCorrectAnswer": true, "marks": 1, "scripts": {}}], "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "gapfill", "marks": 0, "steps": [{"variableReplacementStrategy": "originalfirst", "prompt": "<p>The sum of an arithmetic sequence $a_1, a_2, \\ldots, a_n$ is calculated by the following formula.</p>\n<p>\\[\\sum\\limits_{i=1}^n{a_i}=\\frac{n}{2}(a_1+a_n)\\text{.}\\]</p>", "variableReplacements": [], "showFeedbackIcon": true, "scripts": {}, "type": "information", "marks": 0, "showCorrectAnswer": true}], "showCorrectAnswer": true}], "tags": ["Arithmetic sequences", "Arithmetic Sequences", "arithmetic sequences", "nth term", "partial sums", "random names", "sequences", "taxonomy"], "variablesTest": {"maxRuns": 100, "condition": ""}}, {"name": "Worksheet 1(The time value of Money)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Swa Lup", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/2902/"}], "variables": {"interest": {"name": "interest", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "({value1}-{value})6/{value}"}, "value4": {"name": "value4", "templateType": "randrange", "group": "Ungrouped variables", "description": "", "definition": "random(2000..3000#500)"}, "int": {"name": "int", "templateType": "number", "group": "Ungrouped variables", "description": "", "definition": "6"}, "month": {"name": "month", "templateType": "number", "group": "Ungrouped variables", "description": "", "definition": "4"}, "int2": {"name": "int2", "templateType": "randrange", "group": "Ungrouped variables", "description": "", "definition": "random(9..10#0.5)"}, "n": {"name": "n", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "log({value5}/{value4})/log(1+{int3}/100)"}, "int6": {"name": "int6", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "(e^({int5}/100)-1)100"}, "value": {"name": "value", "templateType": "randrange", "group": "Ungrouped variables", "description": "", "definition": "random(4000..6000#500)"}, "value5": {"name": "value5", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "{value4}+1000"}, "value1": {"name": "value1", "templateType": "randrange", "group": "Ungrouped variables", "description": "", "definition": "random(7000..9000#500)"}, "value2": {"name": "value2", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "{value}0.06/4"}, "int5": {"name": "int5", "templateType": "randrange", "group": "Ungrouped variables", "description": "", "definition": "random(5..6#0.1)"}, "int4": {"name": "int4", "templateType": "randrange", "group": "Ungrouped variables", "description": "", "definition": "random(7..9#0.5)"}, "int1": {"name": "int1", "templateType": "randrange", "group": "Ungrouped variables", "description": "", "definition": "random(9..9.5#0.1)"}, "year": {"name": "year", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "{value6}/(1+{int4}/100)^{years}"}, "value3": {"name": "value3", "templateType": "randrange", "group": "Ungrouped variables", "description": "", "definition": "random(1000..1500#50)"}, "value6": {"name": "value6", "templateType": "randrange", "group": "Ungrouped variables", "description": "", "definition": "random(6500..7000#100)"}, "interest1": {"name": "interest1", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "{intdec}36500/360"}, "int3": {"name": "int3", "templateType": "randrange", "group": "Ungrouped variables", "description": "", "definition": "random(10..12#1)"}, "intdec": {"name": "intdec", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "{int1}/100"}, "amount": {"name": "amount", "templateType": "anything", "group": "Ungrouped variables", "description": "", "definition": "{value3}*(1+(133/365)({int2}/100))"}, "years": {"name": "years", "templateType": "randrange", "group": "Ungrouped variables", "description": "", "definition": "random(11..15#1)"}}, "ungrouped_variables": ["value", "value1", "interest", "month", "value2", "int", "int1", "interest1", "intdec", "value3", "int2", "amount", "value4", "value5", "int3", "n", "value6", "int4", "years", "year", "int5", "int6"], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": ""}, "variable_groups": [], "preamble": {"css": "", "js": ""}, "functions": {}, "tags": [], "statement": "<p></p>\n<p></p>", "variablesTest": {"condition": "", "maxRuns": 100}, "parts": [{"sortAnswers": false, "marks": 0, "showCorrectAnswer": true, "prompt": "<p>Suppose a loan of&nbsp;&pound;{value} is to be repaid by the amount of&nbsp;&pound;{value1} at the end of two months. What is the annual rate of simple interest,i in %?&nbsp;</p>\n<p>[[0]]%</p>", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "gaps": [{"notationStyles": ["plain", "en", "si-en"], "marks": 1, "showCorrectAnswer": true, "minValue": "{interest}-0.1", "maxValue": "{interest}+0.1", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "allowFractions": false, "mustBeReduced": false, "unitTests": [], "mustBeReducedPC": 0, "type": "numberentry", "correctAnswerFraction": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain"}], "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "showFeedbackIcon": true, "type": "gapfill"}, {"sortAnswers": false, "marks": 0, "showCorrectAnswer": true, "prompt": "<p>How long does it take for&nbsp;&pound;{value} to earn&nbsp;&pound;{value2} at {int}% p.a simple interest? Answer in %</p>\n<p>[[0]]%</p>", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "gaps": [{"notationStyles": ["plain", "en", "si-en"], "marks": 1, "showCorrectAnswer": true, "minValue": "{month}", "maxValue": "{month}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "allowFractions": false, "mustBeReduced": false, "unitTests": [], "mustBeReducedPC": 0, "type": "numberentry", "correctAnswerFraction": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain"}], "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "showFeedbackIcon": true, "type": "gapfill"}, {"sortAnswers": false, "marks": 0, "showCorrectAnswer": true, "prompt": "<p>The yield on a deposit is {int1}% on the ACT/360 basis. What is the equivalent yield on an ACT/365 basis? Answer in %</p>\n<p>[[0]]%</p>", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "gaps": [{"notationStyles": ["plain", "en", "si-en"], "marks": 1, "showCorrectAnswer": true, "minValue": "{interest1}", "maxValue": "{interest1}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "allowFractions": false, "mustBeReduced": false, "unitTests": [], "mustBeReducedPC": 0, "type": "numberentry", "correctAnswerFraction": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain"}], "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "showFeedbackIcon": true, "type": "gapfill"}, {"sortAnswers": false, "marks": 0, "showCorrectAnswer": true, "prompt": "<p>&pound;{value3} is deposited with a bank on 10 May 2014 and withdrawn at the same time of the day on 20 september 2014. Find the accumulated value if the interest rate is {int2}% simple interest.</p>\n<p>&pound;[[0]]</p>", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "gaps": [{"notationStyles": ["plain", "en", "si-en"], "marks": 1, "showCorrectAnswer": true, "minValue": "{amount}-1", "maxValue": "{amount}+1", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "allowFractions": false, "mustBeReduced": false, "unitTests": [], "mustBeReducedPC": 0, "type": "numberentry", "correctAnswerFraction": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain"}], "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "showFeedbackIcon": true, "type": "gapfill"}, {"sortAnswers": false, "marks": 0, "showCorrectAnswer": true, "prompt": "<p>How long will it take for &pound;{value4} to accumulate to &pound;{value5} at {int3}% p.a? [[0]] Years</p>", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "gaps": [{"notationStyles": ["plain", "en", "si-en"], "marks": 1, "showCorrectAnswer": true, "minValue": "{n}", "maxValue": "{n}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "allowFractions": false, "mustBeReduced": false, "unitTests": [], "mustBeReducedPC": 0, "type": "numberentry", "correctAnswerFraction": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain"}], "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "showFeedbackIcon": true, "type": "gapfill"}, {"sortAnswers": false, "marks": 0, "showCorrectAnswer": true, "prompt": "<p>A necklace is appraised at&nbsp;&pound;{value6}. If the value of the necklace has increased at an annual rate of {int4}%, how much was it worth {years} years ago?&nbsp;</p>\n<p>&pound;&nbsp;[[0]]</p>", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "gaps": [{"notationStyles": ["plain", "en", "si-en"], "marks": 1, "showCorrectAnswer": true, "minValue": "{year}", "maxValue": "{year}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "allowFractions": false, "mustBeReduced": false, "unitTests": [], "mustBeReducedPC": 0, "type": "numberentry", "correctAnswerFraction": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain"}], "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "showFeedbackIcon": true, "type": "gapfill"}, {"sortAnswers": false, "marks": 0, "showCorrectAnswer": true, "prompt": "<p>Suppose, force of interest,&nbsp;&delta; = {int5}%. What is the effective annual rate of interest? Answer in %.&nbsp;</p>\n<p>[[0]]%</p>", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "gaps": [{"notationStyles": ["plain", "en", "si-en"], "marks": 1, "showCorrectAnswer": true, "minValue": "{int6}", "maxValue": "{int6}", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "allowFractions": false, "mustBeReduced": false, "unitTests": [], "mustBeReducedPC": 0, "type": "numberentry", "correctAnswerFraction": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain"}], "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "showFeedbackIcon": true, "type": "gapfill"}, {"sortAnswers": false, "marks": 0, "showCorrectAnswer": true, "prompt": "<p>If a fund of&nbsp;&pound;1 accumulates at a force of&nbsp;&delta;(t)=0.02t, find the accumulated amount over 2 years as well as the annual effective rate of interest.</p>\n<p>Accumulated amount:[[0]]</p>\n<p>interest rate in %:[[1]]%</p>", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "gaps": [{"notationStyles": ["plain", "en", "si-en"], "marks": 1, "showCorrectAnswer": true, "minValue": "1.0408", "maxValue": "1.0408", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "allowFractions": false, "mustBeReduced": false, "unitTests": [], "mustBeReducedPC": 0, "type": "numberentry", "correctAnswerFraction": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain"}, {"notationStyles": ["plain", "en", "si-en"], "marks": 1, "showCorrectAnswer": true, "minValue": "2.02", "maxValue": "2.02", "variableReplacementStrategy": "originalfirst", "variableReplacements": [], "scripts": {}, "extendBaseMarkingAlgorithm": true, "customMarkingAlgorithm": "", "allowFractions": false, "mustBeReduced": false, "unitTests": [], "mustBeReducedPC": 0, "type": "numberentry", "correctAnswerFraction": false, "showFeedbackIcon": true, "correctAnswerStyle": "plain"}], "customMarkingAlgorithm": "", "unitTests": [], "scripts": {}, "showFeedbackIcon": true, "type": "gapfill"}], "advice": "<p>$1+i=(1+\\frac{i^{(p)}}{p})^p$</p>\n<p>$1+i=e^{\\delta }$</p>\n<p>$v_{i}=\\frac{1}{1+i}=e^{-\\delta }$</p>\n<p>$d=1-v_{i}$</p>\n<p>$A(n)=1+in$</p>\n<p>$A(n)={(1+i)}^n$</p>\n<p>$A(n)=(1+\\frac{i^{(p)}}{p})^{pn}$</p>\n<p>$A(n)=e^{{\\delta}n}$</p>\n<p>$A(n)=e^{\\int_{0}^{n}\\delta (t) dt)}$</p>\n<p>$1+i_M=(1+i_R)(1+q)$</p>", "rulesets": {}, "type": "question"}]}], "timing": {"timedwarning": {"action": "none", "message": ""}, "timeout": {"action": "none", "message": ""}, "allowPause": true}, "showQuestionGroupNames": false, "duration": 0, "name": "Sharika's copy of Numerical reasoning - money (printed worksheet)", "feedback": {"showtotalmark": false, "showactualmark": false, "advicethreshold": 0, "intro": "", "feedbackmessages": [], "allowrevealanswer": false, "showanswerstate": false, "enterreviewmodeimmediately": false, "showexpectedanswerswhen": "never", "showpartfeedbackmessageswhen": "never", "showactualmarkwhen": "never", "showtotalmarkwhen": "never", "showanswerstatewhen": "never", "showadvicewhen": "never"}, "metadata": {"description": "<p>Questions about percentage and ratio, applied to finance.</p>\n                <p>Based on section 3.2 of the Maths-Aid workbook on numerical reasoning.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "navigation": {"preventleave": true, "reverse": true, "onleave": {"action": "none", "message": ""}, "showfrontpage": true, "startpassword": "", "allowregen": false, "showresultspage": "never", "browse": true}, "showstudentname": true, "percentPass": 0, "type": "exam", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}, {"name": "Sharika Mesba", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3475/"}], "extensions": ["random_person"], "custom_part_types": [], "resources": []}