Difference between revisions of "2016 AMC 8 Problems/Problem 12"
Hashtagmath (talk | contribs) |
Notmyopic667 (talk | contribs) (→Problem) |
||
Line 1: | Line 1: | ||
− | ==Problem== | + | ==Problem 12== |
− | Jefferson Middle School has the same number of boys and girls. | + | Jefferson Middle School has the same number of boys and girls. <math>\frac{3}{4}</math> of the girls and <math>\frac{2}{3}</math> |
+ | of the boys went on a field trip. What fraction of the students on the field trip were girls? | ||
<math>\textbf{(A) }\frac{1}{2}\qquad\textbf{(B) }\frac{9}{17}\qquad\textbf{(C) }\frac{7}{13}\qquad\textbf{(D) }\frac{2}{3}\qquad \textbf{(E) }\frac{14}{15}</math> | <math>\textbf{(A) }\frac{1}{2}\qquad\textbf{(B) }\frac{9}{17}\qquad\textbf{(C) }\frac{7}{13}\qquad\textbf{(D) }\frac{2}{3}\qquad \textbf{(E) }\frac{14}{15}</math> |
Revision as of 21:30, 22 March 2021
Problem 12
Jefferson Middle School has the same number of boys and girls. of the girls and
of the boys went on a field trip. What fraction of the students on the field trip were girls?
Solutions
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 there be boys and
girls in the school. We see
, which means
kids went on the trip and
kids are girls. So, the answer is
, which is
2016 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 11 |
Followed by Problem 13 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.