// Numbas version: exam_results_page_options
{"name": "Basic Percentages", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"metadata": {"description": "<p>Basic Percentages Question</p>\n<p>rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "functions": {}, "preamble": {"css": "", "js": ""}, "ungrouped_variables": ["a", "b", "ans", "c", "d", "ans1", "ans2", "ans3", "ans4", "z"], "tags": [], "parts": [{"showFeedbackIcon": true, "sortAnswers": false, "useCustomName": false, "prompt": "<p>If $\\var{b}$% of a number is $\\var{a}$,&nbsp;what was the original amount?</p>\n<p>[[0]]</p>", "gaps": [{"minValue": "ans", "allowFractions": false, "showFeedbackIcon": true, "correctAnswerFraction": false, "mustBeReducedPC": 0, "useCustomName": false, "showFractionHint": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "maxValue": "ans", "customName": "", "unitTests": [], "type": "numberentry", "customMarkingAlgorithm": "", "notationStyles": ["plain", "en", "si-en"], "marks": 1, "mustBeReduced": false, "correctAnswerStyle": "plain", "scripts": {}}], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "unitTests": [], "type": "gapfill", "customMarkingAlgorithm": "", "marks": 0, "scripts": {}}, {"showFeedbackIcon": true, "sortAnswers": false, "useCustomName": false, "prompt": "<p>If $\\var{d}$% of a number is $\\var{c}$,&nbsp;what was the original amount?</p>\n<p>[[0]]</p>", "gaps": [{"minValue": "ans1", "allowFractions": false, "showFeedbackIcon": true, "correctAnswerFraction": false, "mustBeReducedPC": 0, "useCustomName": false, "showFractionHint": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "maxValue": "ans1", "customName": "", "unitTests": [], "type": "numberentry", "customMarkingAlgorithm": "", "notationStyles": ["plain", "en", "si-en"], "marks": 1, "mustBeReduced": false, "correctAnswerStyle": "plain", "scripts": {}}], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "unitTests": [], "type": "gapfill", "customMarkingAlgorithm": "", "marks": 0, "scripts": {}}, {"showFeedbackIcon": true, "sortAnswers": false, "useCustomName": false, "prompt": "<p>Reduce&nbsp;$\\var{a}$ by $\\var{d}$%</p>\n<p>[[0]]</p>", "gaps": [{"minValue": "ans2", "allowFractions": false, "showFeedbackIcon": true, "correctAnswerFraction": false, "mustBeReducedPC": 0, "useCustomName": false, "showFractionHint": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "maxValue": "ans2", "customName": "", "unitTests": [], "type": "numberentry", "customMarkingAlgorithm": "", "notationStyles": ["plain", "en", "si-en"], "marks": 1, "mustBeReduced": false, "correctAnswerStyle": "plain", "scripts": {}}], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "unitTests": [], "type": "gapfill", "customMarkingAlgorithm": "", "marks": 0, "scripts": {}}, {"showFeedbackIcon": true, "sortAnswers": false, "useCustomName": false, "prompt": "<p>Reduce&nbsp;$\\var{c}$ by $\\var{b}$%</p>\n<p>[[0]]</p>", "gaps": [{"minValue": "ans3", "allowFractions": false, "showFeedbackIcon": true, "correctAnswerFraction": false, "mustBeReducedPC": 0, "useCustomName": false, "showFractionHint": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "maxValue": "ans3", "customName": "", "unitTests": [], "type": "numberentry", "customMarkingAlgorithm": "", "notationStyles": ["plain", "en", "si-en"], "marks": 1, "mustBeReduced": false, "correctAnswerStyle": "plain", "scripts": {}}], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "unitTests": [], "type": "gapfill", "customMarkingAlgorithm": "", "marks": 0, "scripts": {}}, {"showFeedbackIcon": true, "sortAnswers": false, "useCustomName": false, "prompt": "<p>Increase&nbsp;$\\var{a}$ by $\\var{c}$%</p>\n<p>[[0]]</p>", "gaps": [{"minValue": "ans4", "allowFractions": false, "showFeedbackIcon": true, "correctAnswerFraction": false, "mustBeReducedPC": 0, "useCustomName": false, "showFractionHint": true, "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "maxValue": "ans4", "customName": "", "unitTests": [], "type": "numberentry", "customMarkingAlgorithm": "", "notationStyles": ["plain", "en", "si-en"], "marks": 1, "mustBeReduced": false, "correctAnswerStyle": "plain", "scripts": {}}], "showCorrectAnswer": true, "variableReplacementStrategy": "originalfirst", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "customName": "", "unitTests": [], "type": "gapfill", "customMarkingAlgorithm": "", "marks": 0, "scripts": {}}], "rulesets": {}, "variables": {"a": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "a", "definition": "random(2..10)*b"}, "b": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "b", "definition": "random(10..50#10)"}, "ans": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "ans", "definition": "{a}/{b}*100"}, "ans3": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "ans3", "definition": "c*((100-b)/100)"}, "z": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "z", "definition": "(a/100)*d"}, "ans1": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "ans1", "definition": "{c}/{d}*100"}, "c": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "c", "definition": "random(2..10)*d"}, "ans2": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "ans2", "definition": "a*((100-d)/100)"}, "ans4": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "ans4", "definition": "a*((100+c)/100)"}, "d": {"group": "Ungrouped variables", "description": "", "templateType": "anything", "name": "d", "definition": "random(10..50#10)"}}, "variablesTest": {"maxRuns": 100, "condition": ""}, "variable_groups": [], "statement": "", "extensions": [], "advice": "<p><span style=\"text-decoration: underline;\"><strong>Parts a and b</strong></span></p>\n<p>To answer this question, we need to first find $1$% and then multiply by $100$ to get to the original amount.</p>\n<p>This is given by the formula: $\\frac{\\text{Amount given}}{\\text{Percentage}} \\times 100$</p>\n<p>In part a, $\\frac{\\var{a}}{\\var{b}} \\times 100 = \\var{ans}$</p>\n<p><span style=\"text-decoration: underline;\"><strong>Parts c, d, and e</strong></span></p>\n<p><span style=\"text-decoration: underline;\"></span>For these parts you need to find the percentage given of the original amount first.</p>\n<p>For part c this is $\\frac{\\var{a}}{{100}}\\times\\var{d} = \\var{z}$. (Remember you can use your own method to do this, you don't necessarily have to follow this one!)</p>\n<p>Then, you subtract (if it is a reduction) or add (if it is an increase) to the original amount: $\\var{a} - \\var{z} = \\var{ans2}$</p>", "name": "Basic Percentages", "contributors": [{"name": "Mark Hodds", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/510/"}, {"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}]}], "contributors": [{"name": "Mark Hodds", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/510/"}, {"name": "TEAME CIT", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/591/"}]}