2016 AMC 8

Complete problem set with solutions and individual problem pages

Problem 12 Medium

Jefferson Middle School has the same number of boys and girls. \frac{3}{4} of the girls and \frac{2}{3} of the boys went on a field trip. What fraction of the students on the field trip were girls?

  • A.

    \frac12

  • B.

    \frac{9}{17}

  • C.

    \frac{7}{13}

  • D.

    \frac{2}{3}

  • E.

    \frac{14}{15}

Answer:B

Solution 1

Let there be b boys and g girls in the school. We see g=b, which means \frac{3}{4}b+\frac{2}{3}b=\frac{17}{12}b kids went on the trip and \frac{3}{4}b kids are girls. So, the answer is \frac{\frac{3}{4}b}{\frac{17}{12}b}=\frac{9}{17}, which is \boxed{\textbf{(B)} \frac{9}{17}}.

 

Solution 2

Using WLOG (Without loss of generativity), Let there be 12 boys and 12 girls in the school. Now we can do \frac{3}{4}\times{12} + \frac{2}{3}\times{12} to get the total number of students going to the field trip to be 17. Since we already know the number of girls to be 9. We have our answer to be \frac{9}{17}. So, the answer is \boxed{\textbf{(B)} \frac{9}{17}}.

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