// Numbas version: exam_results_page_options {"name": "Numerical reasoning - percentages and profit", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"commanumber": {"definition": "var parts=n.toString().split(\".\");\n return parts[0].replace(/\\B(?=(\\d{3})+(?!\\d))/g, \",\") + (parts[1] ? \".\" + parts[1] : \"\");", "type": "string", "language": "javascript", "parameters": [["n", "number"]]}, "lcommanumber": {"definition": "var parts=n.toString().split(\".\");\n return parts[0].replace(/\\B(?=(\\d{3})+(?!\\d))/g, \",\\\\!\") + (parts[1] ? \".\" + parts[1] : \"\");", "type": "string", "language": "javascript", "parameters": [["n", "number"]]}}, "name": "Numerical reasoning - percentages and profit", "tags": ["maths-aid", "money", "numerical reasoning", "profit"], "advice": "

First, work out the profit made on the original product.

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The original production cost was $\\var{produce}$ {pence} per unit. The profit per unit was $\\var{sell}-\\var{produce} = \\var{sell-produce}$ {pence} per unit.

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{commanumber(units1)} units of the original product were sold per month, so the total profit per month was

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\\[ \\var{latex(lcommanumber(units1))} \\times \\var{sell-produce} \\var{p} = \\var{latex(lcommanumber(profit1))} \\var{p} = \\var{latex(texpounds)} \\var{latex(lcommanumber(profit1/100))}. \\]

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Now work out the cost of producing the new product. The new product costs $\\var{percent}\\%$ more. $\\var{percent}\\%$ of $\\var{produce} = \\simplify{{percent}/100}$ of $\\var{produce} = \\var{produce2-produce}\\var{p}$.

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So the new production cost is $\\var{produce} + \\var{produce2-produce} = \\var{produce2} \\var{p}$. The profit per unit is now $\\var{sell} - \\var{produce2} = \\var{sell-produce2} \\var{p}$.

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{commanumber(units2)} units of the new product were sold per month, so the total profit per month is now

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\\[ \\var{latex(lcommanumber(units2))} \\times \\var{sell-produce2} \\var{p} = \\var{latex(lcommanumber(profit2))} \\var{p} = \\var{latex(texpounds)} \\var{latex(lcommanumber(profit2/100))}. \\]

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So the added profit is $\\var{latex(texpounds)}\\var{latex(lcommanumber(profit2/100))} - \\var{latex(texpounds)}\\var{latex(lcommanumber(profit1/100))} = \\var{latex(texpounds)}\\var{latex(lcommanumber(extraprofit))}.$

", "rulesets": {}, "parts": [{"prompt": "

If the manufacturer's selling price in each instance was {sell} {pence} per unit, what was the manufacturer's added profit per month with the newer product?

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{pounds} [[0]]

", "gaps": [{"minvalue": "extraprofit", "type": "numberentry", "maxvalue": "extraprofit", "marks": 1.0, "showPrecisionHint": false}], "type": "gapfill", "marks": 0.0}], "extensions": [], "statement": "

A product costing {produce} {pence} per unit to produce had been selling at the average rate of {commanumber(units1)} units per month.

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After the product was improved, sales increased to an average of {commanumber(units2)} units per month. However, the new product cost {percent} percent more to produce.

", "variable_groups": [], "progress": "ready", "type": "question", "variables": {"sell": {"definition": "produce+random(20..40#5)", "name": "sell"}, "units1": {"definition": "random(1..15)*mult", "name": "units1"}, "units2": {"definition": "ceil(profit1/(sell-produce2)/mult)*mult+random(1..8)*mult", "name": "units2"}, "produce2": {"definition": "produce*diff", "name": "produce2"}, "pounds": {"definition": "currency[0]", "name": "pounds"}, "texpounds": {"definition": "latex(if(pounds='$','\\\\$',pounds))", "name": "texpounds"}, "percent": {"definition": "(diff-1)*100", "name": "percent"}, "pence": {"definition": "currency[1]", "name": "pence"}, "p": {"definition": "currency[2]", "name": "p"}, "produce": {"definition": "random(40..95#5)", "name": "produce"}, "extraprofit": {"definition": "(profit2-profit1)/100", "name": "extraprofit"}, "diff": {"definition": "random(1.05..floor(20*sell/produce)/20#0.05)", "name": "diff"}, "currency": {"definition": "random(['$','cents','\u00a2'],['\u00a3','pence','p'],['\u20ac','cents','c'])", "name": "currency"}, "profit1": {"definition": "units1*(sell-produce)", "name": "profit1"}, "mult": {"definition": "10^random(3,4,5)", "name": "mult"}, "profit2": {"definition": "ceil(units2*(sell-produce2))", "name": "profit2"}}, "metadata": {"notes": "", "description": "

Given cost of production and price of sale of a product; a percentage increase in cost of production; and unit sales before and after; work out the extra profit.

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Based on question 6 from section 3 of the maths-aid workbook on numerical reasoning.

", "licence": "Creative Commons Attribution 4.0 International"}, "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}]}], "contributors": [{"name": "Christian Lawson-Perfect", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/7/"}]}