// Numbas version: finer_feedback_settings
{"name": "Q5 Calculating tax credit", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["standard", "higher", "salary", "name", "tax", "cut", "ans"], "name": "Q5 Calculating tax credit", "tags": ["rebelmaths"], "advice": "<p>First calculate the gross income tax:</p>\n<p><em>standard rate:</em></p>\n<p>$\\var{cut} \\times (\\frac{\\var{standard}}{100})$</p>\n<p><em>higher rate:</em></p>\n<p>$(\\var{salary}-\\var{cut})&nbsp;\\times (\\frac{\\var{higher}}{100})$</p>\n<p><em>gross income tax = standard rate + higher rate</em></p>\n<p>Then remember,</p>\n<p>income tax =&nbsp;&nbsp;gross income tax - tax credit</p>\n<p>=&gt; tax credit = gross income tax - income tax</p>\n<p>or mathematically:</p>\n<p><strong>$((\\var{cut}&nbsp;\\times \\frac{\\var{standard}}{100}) +((\\var{salary}-\\var{cut})&nbsp;\\times \\frac{\\var{higher}}{100})) - \\var{tax} = &euro;\\var{ans}$</strong></p>", "rulesets": {}, "parts": [{"stepsPenalty": "1", "prompt": "<p>$\\var{name}$ has an annual salary of &euro;$\\var{salary}$ and&nbsp;her standard cut-off point is &euro;$\\var{cut}$. The standard rate of income tax is $\\var{standard}$% and the higher rate is $\\var{higher}$%. If&nbsp;she pays &euro;$\\var{tax}$ in income tax for the year, calculate her tax credit.</p>\n<p>&euro;[[0]]</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"precisionType": "dp", "precisionMessage": "You have not given your answer to the correct precision.", "allowFractions": false, "variableReplacements": [], "precision": "2", "maxValue": "{ans}", "minValue": "{ans}", "variableReplacementStrategy": "originalfirst", "strictPrecision": false, "correctAnswerFraction": false, "showCorrectAnswer": true, "precisionPartialCredit": 0, "scripts": {}, "marks": "2", "type": "numberentry", "showPrecisionHint": false}], "steps": [{"prompt": "<p>First calculate the gross income tax:</p>\n<p><em>standard rate:</em></p>\n<p>x * ({standard}/100)</p>\n<p><em>higher rate:</em></p>\n<p>y * ({higher}/100)</p>\n<p><em>gross income tax = standard rate + higher rate</em></p>\n<p>Then remember,</p>\n<p><em>income tax =&nbsp;&nbsp;gross income tax - tax credit</em></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}, {"prompt": "<p>First consider the first $\\var{cut}$ euro of her income. Calculate&nbsp;$\\var{standard}$% of&nbsp;$\\var{cut}$.</p>\n<p>Find how much money is taxed at the higher rate and find&nbsp;$\\var{higher}$% of this.</p>\n<p>Now you can find her gross tax.</p>\n<p>gross tax - credit = net tax. If we move this around we get credit = gross tax - net tax</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 0, "scripts": {}, "showCorrectAnswer": true, "type": "gapfill"}], "extensions": [], "statement": "<p>Calculate to the nearest euro:</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"salary": {"definition": "random(40000..55000#1000)", "templateType": "anything", "group": "Ungrouped variables", "name": "salary", "description": ""}, "cut": {"definition": "random(28000..({salary}-15000)#500)", "templateType": "anything", "group": "Ungrouped variables", "name": "cut", "description": ""}, "name": {"definition": "random('Susan','Rose','Lisa','Karen','Kate','Vicky')", "templateType": "anything", "group": "Ungrouped variables", "name": "name", "description": ""}, "tax": {"definition": "random(6500..9000#50)", "templateType": "anything", "group": "Ungrouped variables", "name": "tax", "description": ""}, "standard": {"definition": "random(20..23#0.5)", "templateType": "anything", "group": "Ungrouped variables", "name": "standard", "description": ""}, "ans": {"definition": "({cut}*({standard}/100)+({salary}-{cut})*({higher}/100))-{tax}", "templateType": "anything", "group": "Ungrouped variables", "name": "ans", "description": ""}, "higher": {"definition": "random(35..43)", "templateType": "anything", "group": "Ungrouped variables", "name": "higher", "description": ""}}, "metadata": {"description": "<p>Tax credits</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}]}], "contributors": [{"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}