2016 AMC 8 Problem 12

Attempt Problem 12 of the 2016 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2016 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

12.

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 on the field trip were girls?
12 \dfrac{1}{2}
917 \dfrac{9}{17}
713 \dfrac{7}{13}
23 \dfrac{2}{3}
1415 \dfrac{14}{15}
Answer: B
Concepts:fractionratio and proportion
Small hint:
Choose a convenient equal number of boys and girls.
Big hint:
Using 1212 boys and 1212 girls makes both fractions whole numbers.
Video solution:
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Written solution:
Suppose there are 1212 girls and 1212 boys. Then 99 girls and 88 boys go on the field trip, so the fraction of field-trip students who are girls is 99+8=917.\dfrac{9}{9+8}=\dfrac9{17}.
Thus, B is the correct answer.
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