## 2480.11 – A Birthday Present in Dimes and Quarters

Hartley and Bertha are pooling their money to buy their mother a birthday present. (Her birthday, by coincidence, is the day she was elected to the school board.) The two have $20.25 between them. Hartley has all of his money in dimes and Bertha's is in quarters. Hartley has twice as many dimes as Bertha has quarters. How much money is Hartley contributing?

## Solution

Say Hartley has $2x$ dimes and Bertha has $x$ quarters. Then their money is $2x(0.10) + x(0.25) = 20.25$, so that

$20x + 25x = 2025,$

or $45x = 2025$ and $x = 45.$ So Bertha has 45 quarters and Hartley has 90 dimes.

Check: $45(0.25) = 11.25$ and $90(0.10) = 9.00$. These sum to $20.25.