# math

Julia had 150 fewer bonus points than Kelly.Bothgirls used tthe same number of bonus points. Julia was left with 1 out of 2 of her bonus pointand Kelly was left with 3 out of 4 of her bonus points.how many bonus did Kelly have at first

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1. Kelly's original number of bonus point --- x
Julia's original number of bonus points -- x-150

let the number used by both be y each.

now Kelly has x - y
Julia has x-150 - y

for Kelly:
(x-y)/x = 3/4
4x - 4y = 3x
x - 4y = 0 or x = 4y

for Julia:
(x-150-y)/(x-150) = 1/2
2x - 300 - 2y = x- 150
x - 2y = 150

but x = 4y
4y - 2y = 150
y = 75
then x = 4(75) = 300

so originally,

check:
so they each used up 75
leaving Kelly with 225 and Julia with 75

Does Julia have 1/2 or her original ? YES
Does Kelly have 3/4 of her original ? YES

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