A two-stroke fuel is mixed using the fuel to oil ratio {twostrokefuel}:1.
\nThis is equivalent to the ratio [[0]] : {twostrokeoil}.
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These questions are similar to equivalent fractions. To create an equivalent ratio, you need to multiply (or divide) by the same number on both sides.
\n\nFor example, suppose your ratio is $4:5$ and you are asked to find an equivalent ratio that looks like $?:30$. To get from a 5 to a 30 we can multiply by 6, but to keep the ratio equivalent we need to do the same to the other side of the ratio. So we multiply 4 by 6 and get 24 and we can say the ratios $4:5$ and $24:30$ are equivalent.
\n\nAs a more complicated example, suppose we need to find an equivalent ratio of $4:5$ in the form $31:?$. We need to get from a 4 to a 31 by multiplying or dividing. The easiest way to do this is probably to divide by 4 and then multiply by 31 (note, this is the same as multiplying by $\\frac{31}{4}$). We need to do the same thing to the other side of the ratio. So we multiply 5 by $\\frac{31}{4}$ and get $\\frac{155}{4}$ and we can say the ratios $4:5$ and $31:\\frac{155}{4}$ are equivalent.
\n"}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{ans1}", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"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": "A fixed gear bike is set up in such a way that one revolution of the pedals moves the bike {onedistance} metres. To ride the bike {requireddistance} metres how many revolutions of the pedals are required?
\n[[0]] revolutions.
\nNote: If the answer has many decimal places leave your answer as a fraction (using / as the fraction bar) so that your answer is exact (and not an approximation/rounded-answer)
", "stepsPenalty": "0", "steps": [{"type": "information", "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": "These questions are similar to equivalent fractions. To create an equivalent ratio, you need to multiply (or divide) by the same number on both sides.
\n\nFor example, suppose your ratio is $4:5$ and you are asked to find an equivalent ratio that looks like $?:30$. To get from a 5 to a 30 we can multiply by 6, but to keep the ratio equivalent we need to do the same to the other side of the ratio. So we multiply 4 by 6 and get 24 and we can say the ratios $4:5$ and $24:30$ are equivalent.
\n\nAs a more complicated example, suppose we need to find an equivalent ratio of $4:5$ in the form $31:?$. We need to get from a 4 to a 31 by multiplying or dividing. The easiest way to do this is probably to divide by 4 and then multiply by 31 (note, this is the same as multiplying by $\\frac{31}{4}$). We need to do the same thing to the other side of the ratio. So we multiply 5 by $\\frac{31}{4}$ and get $\\frac{155}{4}$ and we can say the ratios $4:5$ and $31:\\frac{155}{4}$ are equivalent.
\n"}], "gaps": [{"type": "jme", "useCustomName": false, "customName": "", "marks": 1, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "answer": "{requireddistance}/{onedistance}", "showPreview": false, "checkingType": "absdiff", "checkingAccuracy": 0.001, "failureRate": 1, "vsetRangePoints": 5, "vsetRange": [0, 1], "checkVariableNames": false, "singleLetterVariables": false, "allowUnknownFunctions": true, "implicitFunctionComposition": false, "caseSensitive": false, "valuegenerators": []}], "sortAnswers": false}, {"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": "A cordial is mixed using the syrup to water ratio {cordialratio[0]}:{cordialratio[1]}. You need to make {totalcordial} litres. How many litres of syrup do you need?
\n[[0]] L
\nNote: If the answer has many decimal places leave your answer as a fraction (using / as the fraction bar) so that your answer is exact (and not an approximation/rounded-answer)
", "stepsPenalty": "0", "steps": [{"type": "information", "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": "Determine the total number of parts used in the ratio. Find what one part corresponds to and then multiply by the required number of parts.
\n\nFor example, suppose you need to divide 490 kg into the ratio 2:5. The ratio has 7 parts (2+5). One part corresponds to $\\frac{490}{7}=70$ kg. This means 2 parts corresponds to $2\\times 70=140$ kg, and 5 parts corresponds to $5\\times 70=350$ kg. Therefore, 490 kg divided into the ratio 2:5 is 140
Three people split \\${totaldollars} amongst themselves in the ratio {part1}:{part2}:{part3}. How much money does the {position[0]} person get?
\n\\$ [[0]] (to the nearest cent)
", "stepsPenalty": "0", "steps": [{"type": "information", "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": "Determine the total number of parts used in the ratio. Find what one part corresponds to and then multiply by the required number of parts.
\n\nFor example, suppose you need to divide 800 kg into the ratio 2:5:1. The ratio has 8 parts (2+5+1). One part corresponds to $\\frac{800}{8}=100$ kg. This means 2 parts corresponds to $2\\times 100=200$ kg and 5 parts corresponds to $5\\times 100=500$ kg. Therefore, 800 kg divided into the ratio 2:5:1 is 200 kg : 500 kg : 100 kg.
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