Question

At a concert, 2/7 of the audience were men and 2/5 of the remaining audience were women.The rest were children.

a) what fraction of the audience were children?

b) If there were 42 children, how many people were in the audience?

Answer 1

Suppose we had x people in the audience
If 2/7x were men, then 5/7x of the group were non-men

women = (2/5)(5/7x) = 2/7x of the group were women
but 2/7x + 2/7x = 4/7x <--- men and women
which means there were 3/7x children
fraction of audience which were children
= (3/7x) / x
= 3/7

b)
If (3/7)x = 42
x = 42(7/3) = 98


check:
(2/7) of 98 were men ---> 28
leaving 70 women and children
(2/5)(70) were women ----> 28 women
children = 70-28 = 42

second check:
what is (3/7) of 98 ?

Answer 2

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