the ratio of boys to girls in the gym is 7:5. when 6 more girls enter the gym, the ratio of boys to girls becomes even. how many boys and girls now in the gym?

2 answers

21 boys, 21 girls.

7:5 - 6 girsl is 21 boys to 15 girls [think -6]
Don't know what you mean by an "even" ratio.
If the two terms are even, they we divide by at least 2, until one of them or both are odd.
A ratio with both terms even is not in lowest terms,
just like a fraction can be reduced if both numerator or denominator are even.

original:
boys -- 7x
girls --- 5x

6 more girls ---
boys = 7x
girls = 5x+6

new ratio = 7x : (5x+6)
let x=2, ratio is 14:16 which is "even", but becomes 7 : 8
let x=3, ratio is 21 : 21 = 1 : 1
let x=4, ratio is 28 : 26 = 14 : 13
Perhaps you consider the last one an "even" ratio

so there were 28 boys and 20 girls
and now we have 28 boys and 26 girls