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 2x2x dimes and Bertha has xx quarters. Then their money is 2x(0.10)+x(0.25)=20.252x(0.10) + x(0.25) = 20.25, so that

20x+25x=202520x + 25x = 2025

or 45x=202545x = 2025 and x=45x = 45. So Bertha has 45 quarters and Hartley has 90 dimes.

Check: 45(0.25)=11.2545(0.25) = 11.25 and 90(0.10)=9.0090(0.10) = 9.00. These sum to $20.25.