Writing systems of equations

Question

Jamal counted 53 coins in dimes and quarters in his coin bank. He had a total of $9.20. Write a system of equations to model the relationship between the number of dime, d, and quarters, q, Jamal had. How many of each coin did Jamal have?

Answer 1

We can make two equations from the information given in the problem. We have 53 total coins which is equal to the number of dimes plus the number of quarters, so our first equation is 53=d+q. Our second equation comes from the total amount of money, $9.20. We know a quarter is $0.25 and a dime is $0.10, so our number of quarters times $0.25 ($0.25q) plus the number of dimes times $0.10 ($.10d) is equal to our total amount of money. Thus the second equation we get is $9.20=$0.25q+$0.10d.

Answer 2

d + q = 53

0.10d + 0.25q = 9.20

Can you solve the system and answer?