SOLUTION: A group containing boys and girls took a test. If exactly 2/3 of the boys and exactly 3/4 of the girls passed the test, and if an equal number of boys and girls passed the test, th

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: A group containing boys and girls took a test. If exactly 2/3 of the boys and exactly 3/4 of the girls passed the test, and if an equal number of boys and girls passed the test, th      Log On


   

Question 286029: A group containing boys and girls took a test. If exactly 2/3 of the boys and exactly 3/4 of the girls passed the test, and if an equal number of boys and girls passed the test, then what fraction of the entire group passed the test?
a 11/16 b 12/17 c 13/18 d 14/19 e 17/23
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A group containing boys and girls took a test.
If exactly 2/3 of the boys and exactly 3/4 of the girls passed the test,
and if an equal number of boys and girls passed the test,
then what fraction of the entire group passed the test?
:
b = total no. of boys
g = total no. of girls
(b+g) = total in group
:
2%2F3b = 3%2F4g
multiply both sides by 12
4(2)b = 3(3)g
8b = 9g
b%2Fg = 9%2F8
Equal boy and girls passed so we can say:
2%2F39 = 3%2F48
6 = 6; therefore 12 represent total that passed
9 + 8 = 17 represents total students
:
12%2F17 fraction that passed