// Numbas version: exam_results_page_options {"name": "Percentages: Finding original values 2", "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 2", "tags": [], "metadata": {"description": "
Calculating the original amount when told that $p\\%$ is $x$. The value given can be non-integer.
", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "statement": "", "advice": "When calculating the percentage of an amount we use the formula:
\n\\[ \\text{New value} = \\text{Original value } \\times \\text{ Percentage in decimal form} \\]
\nSo, to find the original value, we can rearrange this formula:
\n\\[ \\text{Original value} = \\text{New value } \\div \\text{ Percentage in decimal form}. \\]
\nTo convert the percentage to a decimal we divide by 100, so $\\var{p} \\% = \\var{p/100}$.
\nTherefore, if $\\var{p} \\%$ of a value is $\\var{new}$,
\n\\[ \\begin{split}
\\text{Original value} &\\,= \\var{new} \\div \\var{p/100} \\\\ &\\,= \\var{ans}
\\end{split} \\]
Given that {p}% of a value is {new}, what is the original value?
", "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/"}]}