// Numbas version: finer_feedback_settings
{"name": "Simon's copy of Q5  VAT", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variablesTest": {"condition": "", "maxRuns": 100}, "preamble": {"js": "", "css": ""}, "tags": [], "extensions": [], "parts": [{"showCorrectAnswer": true, "scripts": {}, "sortAnswers": false, "customMarkingAlgorithm": "", "marks": 0, "type": "gapfill", "gaps": [{"showPrecisionHint": false, "precisionPartialCredit": 0, "marks": 1, "customMarkingAlgorithm": "", "minValue": "{ansone}", "precisionMessage": "You have not given your answer to the correct precision.", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "precisionType": "dp", "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "correctAnswerStyle": "plain", "precision": "2", "unitTests": [], "allowFractions": false, "correctAnswerFraction": false, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "mustBeReducedPC": 0, "maxValue": "{ansone}", "mustBeReduced": false, "strictPrecision": true}], "prompt": "<p>What is the price before VAT, to the nearest penny?</p>\n<p>&pound;[[0]]</p>", "unitTests": [], "showFeedbackIcon": true, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "stepsPenalty": 0, "steps": [{"prompt": "<p>The price includes VAT already, so the $\\var{VAT}$% has already been added on. So the price of &pound;$\\var{price}$ corresponds to $(100 + \\var{VAT})\\% = \\var{100+VAT}\\%$. One method is to find 1% first and then 100%.&nbsp;</p>", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "variableReplacements": [], "showCorrectAnswer": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "unitTests": [], "customMarkingAlgorithm": "", "marks": 0, "type": "information"}]}, {"showCorrectAnswer": true, "scripts": {}, "sortAnswers": false, "customMarkingAlgorithm": "", "marks": 0, "type": "gapfill", "gaps": [{"showPrecisionHint": false, "precisionPartialCredit": 0, "marks": 1, "customMarkingAlgorithm": "", "minValue": "{anstwo}", "precisionMessage": "You have not given your answer to the correct precision.", "showFeedbackIcon": true, "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "precisionType": "dp", "showCorrectAnswer": true, "scripts": {}, "type": "numberentry", "correctAnswerStyle": "plain", "precision": "2", "unitTests": [], "allowFractions": false, "correctAnswerFraction": false, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "mustBeReducedPC": 0, "maxValue": "{anstwo}", "mustBeReduced": false, "strictPrecision": true}], "prompt": "<p>What will the new price be&nbsp;if the VAT rate changes to $\\var{VATnew}$%?</p>\n<p>&pound;[[0]]</p>", "unitTests": [], "showFeedbackIcon": true, "variableReplacements": [], "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "stepsPenalty": 0, "steps": [{"prompt": "<p>Start with the price before VAT (answer to part a) and add on the new VAT.</p>", "extendBaseMarkingAlgorithm": true, "showFeedbackIcon": true, "variableReplacements": [], "showCorrectAnswer": true, "scripts": {}, "variableReplacementStrategy": "originalfirst", "unitTests": [], "customMarkingAlgorithm": "", "marks": 0, "type": "information"}]}], "variables": {"ansone": {"templateType": "anything", "description": "", "name": "ansone", "group": "Ungrouped variables", "definition": "{price}/({VATa}/100)"}, "VAT": {"templateType": "anything", "description": "", "name": "VAT", "group": "Ungrouped variables", "definition": "random(13,21,22,23)"}, "VATnew": {"templateType": "anything", "description": "", "name": "VATnew", "group": "Ungrouped variables", "definition": "random(20..24 except VAT)"}, "VATnewa": {"templateType": "anything", "description": "", "name": "VATnewa", "group": "Ungrouped variables", "definition": "100 + {VATnew}"}, "price": {"templateType": "anything", "description": "", "name": "price", "group": "Ungrouped variables", "definition": "random(80..250)*(1+(VAT/100))"}, "anstwo": {"templateType": "anything", "description": "", "name": "anstwo", "group": "Ungrouped variables", "definition": "ansone*(1+({VATnew}/100))"}, "VATa": {"templateType": "anything", "description": "", "name": "VATa", "group": "Ungrouped variables", "definition": "100+{VAT}"}}, "advice": "<p><strong>(a)</strong></p>\n<p>The price before including VAT is 100%.</p>\n<p>The price after including VAT of $\\var{VAT}$% is $\\var{VATa}$%</p>\n<p>Therefore, to get the price before VAT (100%), we divide by $\\var{VATa}$ and multiply by 100.&nbsp;</p>\n<p>$(&pound;\\var{price} \\div \\var{VATa}) \\times 100&nbsp; = &pound;\\var{dpformat(ansone,2)}$</p>\n<p></p>\n<p>(Alternative method: this is the same as dividing by $\\var{VATa/100}$. So our answer is $&pound;\\var{price} \\div \\var{VATa/100}&nbsp; = &pound;\\var{dpformat(ansone,2)}$)</p>\n<p><strong>(b)</strong></p>\n<p>Take the price before VAT, the answer from (a).&nbsp;</p>\n<p>We want to find $\\var{VATnewa}\\%$ of $&pound;\\var{dpformat(ansone,2)}$</p>\n<p>We can do this by multiplying it by $\\frac{\\var{VATnewa}}{100}$&nbsp; &nbsp; (or alternatively multiply by&nbsp;$\\var{VATnewa/100}$)</p>\n<p>$\\var{ansone} \\times (\\frac{\\var{VATnewa}}{100}) = &euro;\\var{anstwo}$</p>", "functions": {}, "metadata": {"description": "<p>VAT</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "<p>The price of an item including VAT at $\\var{VAT}$% is &pound;$\\var{price}$.</p>", "variable_groups": [], "name": "Simon's copy of Q5  VAT", "ungrouped_variables": ["VAT", "VATnew", "price", "ansone", "anstwo", "VATa", "VATnewa"], "rulesets": {}, "type": "question", "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}]}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}, {"name": "Simon Thomas", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3148/"}]}