SOLUTION: Hi Jenny set aside a fixed proportion of her salary on food. It was 20% of her salary. When her salary increased by 10% her food expenditure increased by $50. What was her origina

Question 1172492: Hi
Jenny set aside a fixed proportion of her salary on food. It was 20% of her salary. When her salary increased by 10% her food expenditure increased by $50. What was her original salary. Thanks

Found 3 solutions by Theo, greenestamps, MathTherapy:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
let f = what she spent on food
let s = her salary
first equation is f = .2 * s
when her salary increased by 10%, her food expenditure increased by 50 dollars.
second equation is:
f + 50 = .2 * 1.10 * s
in the second equation, replace f with 2 * s from the first equation to get:
.2 * s + 50 = .2 * 1.10 * s
simplify to get:
.2 * s + 50 = .22 * s
subtract .2 * s from both sides of the equation to get:
50 = .02 * s
solve for s to get:
s = 50 / .02 = 2500
her salary was 2500
her food expenditure was .2 * 2500 = 500
when her salary went up 10%, her salary was 2500 * 1.10 = 2750.
her food expenditure went up 50 dollars to be 550.
550 / 2750 = .2
the proportion remained the same, confirming the solution is correct.
the solution is her original salary was 2500 dollars.

Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!

The increase of $50 in her food expenditure was 20% = 1/5 of the increase in her salary, so the increase in her salary was 5($50) = $250.

The increase in her salary was 10% (1/10) of her original salary, so her original salary was 10($250) = $2500.

Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!
Hi
Jenny set aside a fixed proportion of her salary on food. It was 20% of her salary. When her salary increased by 10% her food expenditure increased by $50. What was her original salary. Thanks

Let original salary be S
Then initial food expenditure was: .2S
A 10% increase in salary makes new salary: 1.1S
Since food expenditure increased by $50, new food expenditure = .2S + 50
We then get: .2(1.1S) = .2S + 50
.22S = .2S + 50
.22S - .2S = 50
.02S = 50
Original salary, or
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