Jamie's income is 5/8 of Anna's. Jamie's expenses 1/2 of Anna's. Jamie saved 40% of his income. What  % of his income that Anna saves?

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

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We will assume that Anna's income = X

Then Jamie's income = (5/8) x

Let Anna's expenses = y

Then , Jamies expenses = (1/2) y

==> Anna's Income = Anna's expenses + savings

==> x =  y + (a/100) *x............(1)

==> Jamie's income = jamie's expenses +savings

==> (5/8)x = (1/2)y + (40%)*(5/8)x

==> (5/8)x = (1/2)y + (1/4)x

Then Anna's saves (1/4) her income = 25%

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

Let Anna's income be x. And let expenditure by y.

Then since Jamies income is 5/8 of Anna's, Jamies in come = 5x/8.

Jamies expenses are 1/2 of annas.

So Jamiie's expenditure = (1/2)y.

So Jamies savings = income - espenditure = 5x/8-y/2 but this is equal to 40% of Jamie's income = (40/100)(5x/8)

So 5x/8 - y/2 = (2/5)(5x/8) = x/4

Therefore y/2 = 5x/8-x/4 = 3x/8.

Therefore y =3x/8

Therefore the expenditure of Anna's = y = 3x/8.

Therefore savings of Annas = income - expenditure  x - 3x/8 = 5x/8.

Therefore the percentage of income Anna saves - ( 5x/8 )100/x = 75%.

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