# there were 490 altogether in 2 groups. group A consited of only boys and group b constied of only girls. ther were 2 and a half times as many girls as boys. some girls joined group b and foe every 4 boys in group a 32 more boys jioned the group. the total number og girls was then one third the total number of boys. express the number of girls who jioned group b as a fraction of boys who jioned group a

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1. sorry about the mistyped capitalization. The lines in error should read

a = 1/8 A

and

b = 1/2 * 1/8 a = a/16

and there are 108 boys at the end, not 1-8

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2. Steve, you incorrect, it should be b=5/2a,

because there are more girls than boys in the group.

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3. to begin, A = 5/2 B

a boys joined A
32/4 = 8, so 8A boys joined the group.so, A = 1/8 A

b girls joined B
So, now there are

B+b = 1/3(9A) = 3A
5/2 A + b = 3A
b = 1/2 A
b = 1/2 * 1/8 A = a/16

example:
A=12
B=30

A/4 = 3, so 3*32 = 96 boys joined A, making 1-8 boys in all

B+b = 108/3 = 36
so, 6 girls joined, or 96/16

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