// Numbas version: exam_results_page_options
{"name": "Percentages: Finding original values 1", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"name": "Percentages: Finding original values 1", "tags": [], "metadata": {"description": "<p>Calculating the original amount when told that $p\\%$ is $x$. The value given and the original values are both integers.</p>", "licence": "None specified"}, "statement": "", "advice": "<p>If we know that $\\var{p}\\%$ of a value is $\\var{new}$, it can help to think of the original value as $100\\%$, and then calculate how many times $\\var{p} \\%$ goes into $100 \\%$.</p>\n<p>Since $\\var{p} \\%$ goes into $100 \\%$ $\\var{100/p}$ times ($100 \\div \\var{p} = \\var{100/p}$), this tells us that $\\var{new}$ will also go into the original value $\\var{100/p}$ times.</p>\n<p>Therefore,</p>\n<p>\\[ \\begin{split} \\text{Original value } &amp;\\,= \\var{new} \\times \\var{100/p} \\\\ &amp;\\,= \\var{ans} . \\end{split} \\]</p>", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"p": {"name": "p", "group": "Ungrouped variables", "definition": "random(1,5,10,20,25,50)", "description": "", "templateType": "anything", "can_override": false}, "ans": {"name": "ans", "group": "Ungrouped variables", "definition": "random(100 .. 1000#10)", "description": "", "templateType": "randrange", "can_override": false}, "new": {"name": "new", "group": "Ungrouped variables", "definition": "ans*p*0.01", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "new-round(new)=0", "maxRuns": "40"}, "ungrouped_variables": ["p", "ans", "new"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"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, "prompt": "<p>Given that {p}% of a value is {new}, what is the original value?</p>", "minValue": "ans", "maxValue": "ans", "correctAnswerFraction": false, "allowFractions": false, "mustBeReduced": false, "mustBeReducedPC": 0, "displayAnswer": "", "showFractionHint": true, "notationStyles": ["plain", "en", "si-en"], "correctAnswerStyle": "plain"}], "partsMode": "all", "maxMarks": 0, "objectives": [], "penalties": [], "objectiveVisibility": "always", "penaltyVisibility": "always", "contributors": [{"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}]}]}], "contributors": [{"name": "Ruth Hand", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3228/"}, {"name": "Ben McGovern", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/4872/"}]}