// Numbas version: exam_results_page_options
{"name": "Rounding and estimating calculations - adding up prices in a shop", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Rounding and estimating calculations - adding up prices in a shop", "type": "question", "tags": ["random names", "taxonomy"], "variablesTest": {"condition": "", "maxRuns": 100}, "variables": {"cash": {"templateType": "anything", "name": "cash", "description": "<p>Amount of cash we have.</p>", "definition": "if(can_afford,\n  ceil(total_rounded_up)\n  ,\n  ceil(sum(p)+ice_cream)-1\n)\n  ", "group": "Randoms"}, "can_afford": {"templateType": "anything", "name": "can_afford", "description": "<p>Can we afford all three items?</p>", "definition": "random(true,false)", "group": "Randoms"}, "total_rounded_up": {"templateType": "anything", "name": "total_rounded_up", "description": "<p>Total price of the three items when&nbsp;rounding up.</p>", "definition": "precround(p[0]+0.05,1) + precround(p[1]+0.05,1) + precround(ice_cream,1)", "group": "Randoms"}, "flavour": {"templateType": "anything", "name": "flavour", "description": "<p>Flavour of the ice cream.</p>", "definition": "random(\"strawberry cheesecake\", \"cookie dough\", \"mint chocolate chip\", \"vanilla\", \"raspberry\", \"Neapolitan\")", "group": "Randoms"}, "ice_cream": {"templateType": "anything", "name": "ice_cream", "description": "<p>Price of the ice cream</p>", "definition": "(random(100..380#10)+9)/100", "group": "Randoms"}, "p": {"templateType": "anything", "name": "p", "description": "<p>Prices of the first two items.</p>", "definition": "repeat((random(30..200 #10) + random(1..9))/100,2)", "group": "Randoms"}}, "extensions": [], "functions": {"pounds": {"parameters": [["n", "number"]], "type": "string", "language": "jme", "definition": "if(n>=1,currency(n,\"\u00a3\",\"\"), \"\u00a3\"+dpformat(n,2))"}}, "statement": "<p>Imagine you are shopping&nbsp;at the&nbsp;supermarket. You only have &pound;{cash}&nbsp;in cash.&nbsp;There are&nbsp;two items in your&nbsp;basket so far, costing {currency(p[0],\"&pound;\",\"p\")} and {currency(p[1],\"&pound;\",\"p\")}.</p>\n<p>Just before checkout, you notice a tasty&nbsp;{flavour}&nbsp;ice cream on the shelf. It costs {currency(ice_cream,\"&pound;\",\"p\")}. Can you put this in your&nbsp;basket without going over your limit?</p>", "variable_groups": [{"name": "Randoms", "variables": ["p", "ice_cream", "total_rounded_up", "can_afford", "cash", "flavour"]}, {"name": "Answers", "variables": []}], "parts": [{"scripts": {}, "variableReplacements": [], "marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "gaps": [{"displayColumns": 0, "minMarks": 0, "distractors": ["", ""], "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "choices": ["<p>Round up.</p>", "<p>Round down.</p>"], "showFeedbackIcon": true, "shuffleChoices": false, "matrix": ["1", "0"], "variableReplacements": [], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "maxMarks": 0, "type": "1_n_2"}], "showCorrectAnswer": true, "prompt": "<p>If we don't want to underestimate the total price of these items, do&nbsp;we round the individual prices up, or down?</p>\n<p>[[0]]<em></em></p>", "type": "gapfill"}, {"scripts": {}, "variableReplacements": [], "marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "gaps": [{"correctAnswerFraction": false, "precisionMessage": "You have not given your answer to the correct precision.", "precisionPartialCredit": 0, "scripts": {}, "type": "numberentry", "variableReplacementStrategy": "originalfirst", "allowFractions": false, "precision": "2", "precisionType": "dp", "maxValue": "total_rounded_up", "showFeedbackIcon": true, "minValue": "total_rounded_up", "correctAnswerStyle": "plain", "mustBeReducedPC": 0, "mustBeReduced": false, "notationStyles": ["plain", "en", "si-en"], "showPrecisionHint": false, "marks": 1, "variableReplacements": [], "strictPrecision": false, "showCorrectAnswer": true}], "showCorrectAnswer": true, "prompt": "<p>Estimate the total price if we buy the ice cream, rounding the price of each item to <strong>1 decimal place</strong>.</p>\n<p>&pound; [[0]]</p>\n<p></p>", "type": "gapfill"}, {"scripts": {}, "variableReplacements": [], "marks": 0, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "gaps": [{"displayColumns": 0, "minMarks": 0, "type": "1_n_2", "variableReplacementStrategy": "originalfirst", "displayType": "radiogroup", "choices": ["<p>Yes, we do have enough cash.</p>", "<p>No, we may not have enough.</p>"], "showFeedbackIcon": true, "shuffleChoices": false, "matrix": "if(can_afford,[1,0],[0,1])", "variableReplacements": [], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "maxMarks": 0}], "showCorrectAnswer": true, "prompt": "<p>Can&nbsp;we be sure that we&nbsp;have enough cash to pay for all three items?</p>\n<p>[[0]]</p>", "type": "gapfill"}], "ungrouped_variables": [], "rulesets": {}, "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>Estimate whether you can afford an extra item in a shop by rounding prices to the nearest 10p.</p>"}, "preamble": {"css": "", "js": ""}, "advice": "<h4>a)</h4>\n<p>We want to ensure we won't go over the limit, so it is better to overestimate. If we underestimated, we could potentially think we have enough money when we don't.</p>\n<p>To overestimate our total, we round each price&nbsp;<strong>up</strong>.</p>\n<h4>b)</h4>\n<p><em></em>We round up all our values to 1 decimal place:</p>\n<table>\n<tbody>\n<tr>\n<th>Original prices</th>\n<td>&pound;{p[0]}</td>\n<td>&pound;{p[1]}</td>\n<td>&pound;{ice_cream}</td>\n</tr>\n<tr>\n<th>Rounded up</th>\n<td>{pounds(precround(p[0]+0.05,1))}</td>\n<td>{pounds(precround(p[1]+0.05,1))}</td>\n<td>{pounds(precround(ice_cream,1))}</td>\n</tr>\n</tbody>\n</table>\n<p>Now we calculate the total of these rounded numbers:</p>\n<p>\\[ \\var{pounds(precround(p[0]+0.05,1))} + \\var{pounds(precround(p[1]+0.05,1))} + \\var{pounds(precround(ice_cream,1))} = \\var{pounds(total_rounded_up)}&nbsp;\\]</p>\n<h4>c)</h4>\n<p><em></em>As the estimated&nbsp;total, &pound;{dpformat(total_rounded_up,2)}, is {if(can_afford,'lower','higher')} than &pound;{cash}, we {if(can_afford,'do have','may not have')} enough money to purchase the {flavour} ice cream.</p>", "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}