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{"name": "Lois's copy of Percentages - Non-Calculator Worded Questions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "b", "f", "g", "k", "l", "m", "n", "o", "p", "q", "r", "s", "t", "u", "v", "w", "x", "y", "z", "aa", "bb", "cc", "dd", "ee", "ff", "gg", "hh"], "name": "Lois's copy of Percentages - Non-Calculator Worded Questions", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p>a) Since the budget is a mutiple of &pound;1000, one way to calculate the amount spent on flowers is to find 1% of &pound;{a} and then multiply this by {b}.</p>\n<p>b) One way to tackle this question is to calculate 1% and 10% of the normal price and then use multiples of these amounts to build up the percentage required.</p>\n<p>It can be quicker to&nbsp;note that the sale price is {100-{g}}% of the original price and then calculate this directly rather than calculating the discount and then subtracting it from the original price.</p>\n<p>c) The fraction of thepopulation that voted is $ \\dfrac{\\var{gg}}{\\var{hh}}$, so the percentage who voted is&nbsp;$ \\dfrac{\\var{gg}}{\\var{hh}} \\times 100$.</p>\n<p>d) We can calculate 1% of &pound;{aa} and then multiply this by {z} and add the answer to &pound;{aa}.</p>", "rulesets": {}, "parts": [{"prompt": "<p>A theatre has a monthly budget of &pound;$ \\var{a}$ for for front-of-house expenses. &nbsp;$\\var{b}\\text{%}$ of this budget is spent on flowers. &nbsp;How much is spent on flowers each month?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(b/100)*a", "minValue": "(b/100)*a", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "1", "type": "numberentry", "correctAnswerStyle": "plain"}, {"prompt": "<p>A jumper is normally priced at &pound;$\\var{f}$. A sale offers $\\var{g}\\text{%}$ off the normal price. &nbsp;What is the sale price of the jumper?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "f*(1-(g/100))", "minValue": "f*(1-(g/100))", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "1", "type": "numberentry", "correctAnswerStyle": "plain"}, {"prompt": "<p>In a small village $\\var{gg}$ people turn up to vote in the local election. &nbsp;If there are $\\var{hh}$ residents in the village what percentage of the village turned up to vote?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "((gg)/(hh))*100", "minValue": "((gg)/(hh))*100", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "1", "type": "numberentry", "correctAnswerStyle": "plain"}, {"prompt": "<p>House prices are expected to increase next year by $\\var{z}\\text{%}$. &nbsp;If your house is currently worth &pound;$\\var{aa}$ how much will it be worth this time next year?</p>", "allowFractions": false, "variableReplacements": [], "maxValue": "(aa)*(1+(z/100))", "minValue": "(aa)*(1+(z/100))", "variableReplacementStrategy": "originalfirst", "notationStyles": ["plain", "en", "si-en"], "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": "1", "type": "numberentry", "correctAnswerStyle": "plain"}], "extensions": [], "statement": "<p>Find the answers to the following questions.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"aa": {"definition": "random(80000..350000#1000)  // random price for house", "templateType": "anything", "group": "Ungrouped variables", "name": "aa", "description": ""}, "cc": {"definition": "random(240..450#5) // random price of television", "templateType": "anything", "group": "Ungrouped variables", "name": "cc", "description": ""}, "gg": {"definition": "random(50..hh-1#50) // random number of people who turned up to vote", "templateType": "anything", "group": "Ungrouped variables", "name": "gg", "description": ""}, "ee": {"definition": "random([5,10,20,25,50,200,100]) // random number of steak sales", "templateType": "anything", "group": "Ungrouped variables", "name": "ee", "description": ""}, "bb": {"definition": "random(1..10) // random percentage increase of population", "templateType": "anything", "group": "Ungrouped variables", "name": "bb", "description": ""}, "dd": {"definition": "random(5..30)  // random percentage decrease in cost of TV", "templateType": "anything", "group": "Ungrouped variables", "name": "dd", "description": ""}, "hh": {"definition": "random(200, 400, 800, 1000)  // random number of residents in village", "templateType": "anything", "group": "Ungrouped variables", "name": "hh", "description": ""}, "ff": {"definition": "random(1..ee-1)  // random number of specials that were steak", "templateType": "anything", "group": "Ungrouped variables", "name": "ff", "description": ""}, "a": {"definition": "random(1000..15000#1000)  // random number of thousands between 1000 and 10000 for front of house takings", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "b": {"definition": "random(5..15)  // random percentage of 5 to 15 spent on flowers", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "g": {"definition": "random(5..35) // random percentage off the jumper", "templateType": "anything", "group": "Ungrouped variables", "name": "g", "description": ""}, "f": {"definition": "random(35..65#5) // random price of jumper", "templateType": "anything", "group": "Ungrouped variables", "name": "f", "description": ""}, "k": {"definition": "random(100..50#50) // random number divisible by 50 total number of balls", "templateType": "anything", "group": "Ungrouped variables", "name": "k", "description": ""}, "m": {"definition": "random([5,6,8,10,12])  // random number of hours allocated to English", "templateType": "anything", "group": "Ungrouped variables", "name": "m", "description": ""}, "l": {"definition": "random([20,25])  // random number from list for number of hours in lessons", "templateType": "anything", "group": "Ungrouped variables", "name": "l", "description": ""}, "o": {"definition": "random(18..p-1#6)  // random number for score", "templateType": "anything", "group": "Ungrouped variables", "name": "o", "description": ""}, "n": {"definition": "random(60..80)  // random percentage test score", "templateType": "anything", "group": "Ungrouped variables", "name": "n", "description": ""}, "q": {"definition": "random([0,1]) // random numbr of hours for a test to take", "templateType": "anything", "group": "Ungrouped variables", "name": "q", "description": ""}, "p": {"definition": "random([20,24,25,30,50,60,75,120,150])  // random total of marks in a test", "templateType": "anything", "group": "Ungrouped variables", "name": "p", "description": ""}, "s": {"definition": "random(10..30#5)  // random percentage of extra time granted in the test", "templateType": "anything", "group": "Ungrouped variables", "name": "s", "description": ""}, "r": {"definition": "random(10..50#10) // random number of minutes for a test to take", "templateType": "anything", "group": "Ungrouped variables", "name": "r", "description": ""}, "u": {"definition": "random(10..50#10)  // random starting time for test - minutes", "templateType": "anything", "group": "Ungrouped variables", "name": "u", "description": ""}, "t": {"definition": "random(9,10)  // random starting time for test - hour", "templateType": "anything", "group": "Ungrouped variables", "name": "t", "description": ""}, "w": {"definition": "random(60..600#10)  // random number of people in the group", "templateType": "anything", "group": "Ungrouped variables", "name": "w", "description": ""}, "v": {"definition": "random(30..45)  // random percentage for sample size", "templateType": "anything", "group": "Ungrouped variables", "name": "v", "description": ""}, "y": {"definition": "random(20..80)  // random percentage of ice creams that were strawberry", "templateType": "anything", "group": "Ungrouped variables", "name": "y", "description": ""}, "x": {"definition": "random(20..300#10) // random number of ice creams sold", "templateType": "anything", "group": "Ungrouped variables", "name": "x", "description": ""}, "z": {"definition": "random(1..12) // random percentage increase for house prices", "templateType": "anything", "group": "Ungrouped variables", "name": "z", "description": ""}}, "metadata": {"description": "<p>These are worded questions on percentages. &nbsp;They can be done without a calculator.</p>", "licence": "Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International"}, "type": "question", "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}]}], "contributors": [{"name": "Lois Rollings", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/326/"}]}