Question 1005201: A group of boys and girls sit a test. Exactly 2/3 of the boys and 3/4 of the girls pass the test. If an equal number of boys and girls passed the test, what fraction of the entire group passed the test?
How do you solve this? Thanks.
Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website! .
A group of boys and girls sit a test. Exactly 2/3 of the boys and 3/4 of the girls pass the test.
If an equal number of boys and girls passed the test, what fraction of the entire group passed the test?
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Let b = the number of boys and g = the number of girls in the class.
Then we have  =  , according to the condition.
Let us write it using the common denominator:  =  , or, which is the same,  =  .
It implies that 8b = 9g. (1)
Next, since the numbers 8 and 9 are relatively primes, (1) implies that b is multiple of 9 and g is multiple of 8:
b = 9*n, g = 8*m (2)
with integer n and m.
Then you can re-write (1) in the form
8*9n = 9*8m, or 72n = 72m.
It implies that n = m and, hence,
b = 9n, g = 8n (3)
with some integer n.
Now, the number of those students who passed the test is
 =  =  =  =  = 12n. (5)
The total number of students in the class is
b + g = 9n + 8n = 17n. (6)
Now it is easy to calculate the ratio of those who passed the test to the total number of students in the class. It is (5) divided by (6):
 =  .
Answer. The ratio of those who passed the test to the total number of students in the class is .
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