Difference between revisions of "2016 AMC 8 Problems/Problem 12"
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Solution 2: Let their be <math>b</math> boys and <math>g</math> girls in the school. We see <math>g=b</math>, which mean <math>\frac{3}{4}b+\frac{2}{3}b=\frac{17}{12}b</math> kids went on the trip and <math>\frac{3}{4}b</math> kids are girls. So, the answer is <math>\frac{\frac{3}{4}b}{\frac{17}{12}b}=\frac{9}{17}</math>, which is <math>\boxed{(B) \frac{9}{17}}</math> | Solution 2: Let their be <math>b</math> boys and <math>g</math> girls in the school. We see <math>g=b</math>, which mean <math>\frac{3}{4}b+\frac{2}{3}b=\frac{17}{12}b</math> kids went on the trip and <math>\frac{3}{4}b</math> kids are girls. So, the answer is <math>\frac{\frac{3}{4}b}{\frac{17}{12}b}=\frac{9}{17}</math>, which is <math>\boxed{(B) \frac{9}{17}}</math> | ||
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{{MAA Notice}} | {{MAA Notice}} |
Revision as of 12:07, 23 November 2016
Jefferson Middle School has the same number of boys and girls. Three-fourths of the girls and two-thirds of the boys went on a field trip. What fraction of the students were girls?
Solution
Solution 1:Set the number of children to a number that is divisible by two, four, and three. In this question, the number of children in the school is not a specific number because there are no actual numbers in the question, only ratios.This way, we can calculate the answer without dealing with decimals. is a number that works. There will be girls and boys. So, there will be = girls on the trip and = boys on the trip. The total number of children on the trip is , so the fraction of girls on the trip is or
Solution 2: Let their be boys and girls in the school. We see , which mean kids went on the trip and kids are girls. So, the answer is , which is
2016 AMC 8 (Problems • Answer Key • Resources) | ||
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Followed by Problem 13 | |
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