at a playground, the ratio of boys to girls was 5:6. if 2 over 5 of the boys and 1 over 2 of the girls left, there were 54 children in the playground. how many boys were at the playground at first?

Answer 1

let the number of boys be 5x
let the number of girls be 6x
(notice 5x :6x = 5:6 )

after departures:
number of boys = (3/5)(5x) or 3x
numer of girls = (1/2)(6x) or 3x

then 3x + 3x = 54
x = 9

So at first there were 45 boys and 54 girls

check:
(2/5) of 45 or 18 boys left, leaving 27 boys
(1/2) of 54 girls left, leaving 27 girls
and 27+27 = 54

Answer 2

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