Question

John and Sarah had a total of $816. However, when John increased his savings by 25% and Sarah increased hers by 1/9, their money equaled. How much money did Sarah have originally?

Answer 1

Let Sarah's original amount be S and John's original amount be J.
S + J = 816 ..............(1)
If John saves 1/4 of his original amount he is left with:
\[\large \frac{3}{4}J\]
If Sarah saves 1/9 of her original amount she is left with:
\[\large \frac{8}{9}S\]
It is given that the amounts after savings are deducted are equal. Therefore we can write:
\[\large \frac{3}{4}J=\frac{8}{9}S\ ........(2)\]
Multiplying both sides of equation (2) by 4/3 we get:
\[\large J=\frac{8\times4}{9\times3}S=\frac{32}{27}S\ ...........(3)\]
Plugging the expression for J in (3) into equation (1) gives:
\[\large \frac{32}{27}S+S=816\ ...........(4)\]
Now you just need to solve equation (4) to find S.

Answer 2

Sorry, I think I worded the question incorrectly. They made more money, but i think that it uses the same concept. Thanks!