Given a student discount, calculate a discounted price.
", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "{pname} is buying a new {item}. The price of the model he picked is £{price}. On a website with discounts for students, he found a voucher for a discount of {percentage}%.
", "advice": "There are multiple methods to approach this problem. The first method involves working out the discounted price as a percentage of the original, while the second method calculates the value of the discount and subtracts that from the listed price.
\nThere is a {percentage}% decrease in price. This means that the new price will be {100-percentage}% of the old price.
\n\\[\\begin{align} \\frac{\\var{100-percentage}}{100} \\times \\var{price} &= \\var{(100-percentage)/100*price} \\\\&= \\var{dpformat((100-percentage)/100*price, 2)}\\text{.} \\end{align}\\]
\nOr, using the multiplier method,
\n\\[\\begin{align} \\var{(100-percentage)/100} \\times \\var{price} &= \\var{(100-percentage)/100*price}\\\\&= \\var{dpformat((100-percentage)/100*price, 2)}\\text{.} \\end{align}\\]
\nWhen we are talking about money, it is usually assumed that we will round the answer to 2 decimal places.
\nWe find the discount first. This is
\n\\[\\frac{\\var{percentage}}{100} \\times \\var{price} = \\var{(percentage)/100*price}\\text{.}\\]
\nOr using a decimal multiplier,
\n\\[\\var{(percentage)/100} \\times \\var{price} = \\var{(percentage)/100*price}\\text{.}\\]
\nThen we subtract the discount from the original price to get the new price:
\n\\[ \\var{price} - \\var{dpformat(discount,2)} = \\var{dpformat(price - discount, 2)}\\text{.} \\]
\n", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true}, "constants": [], "variables": {"discount": {"name": "discount", "group": "Ungrouped variables", "definition": "percentage*price/100", "description": "", "templateType": "anything", "can_override": false}, "pname": {"name": "pname", "group": "Ungrouped variables", "definition": "random(\"Josh\", \"Adam\", \"Mike\", \"Trevor\", \"Alex\")", "description": "A male name.
", "templateType": "anything", "can_override": false}, "discountrounded": {"name": "discountrounded", "group": "Ungrouped variables", "definition": "precround(discount,2)", "description": "", "templateType": "anything", "can_override": false}, "price": {"name": "price", "group": "Ungrouped variables", "definition": "switch(\n item = \"TV\", random(170.99..1199.99), \n item = \"laptop\", random(200.99..799.99),\n item = \"smartphone\", random(100.99..799.99),\n item = \"PC\", random(200.99..969.99),\n item = \"gaming console\", random(80.99..349.99),\n random(110.99..649.99))\n", "description": "Price of an item.
", "templateType": "anything", "can_override": false}, "item": {"name": "item", "group": "Ungrouped variables", "definition": "random(\"TV\", \"laptop\", \"smartphone\", \"PC\", \"gaming console\", \"fridge\")", "description": "The bought item.
", "templateType": "anything", "can_override": false}, "percentage": {"name": "percentage", "group": "Ungrouped variables", "definition": "random(5..40 #5)", "description": "Discount percentage.
", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": "1000"}, "ungrouped_variables": ["item", "pname", "price", "percentage", "discount", "discountrounded"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "What will the discounted price of the {item} be?
\nRound your answer to the nearest penny.
\n£ [[0]]
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