Question

Bridget has 33 dimes and quarters in her piggy bank. If the value of these coins is $6.00, how many dimes and quarters does she have? Set up and solve a system of equations to solve the problem. Show your work.

Answer 1

Use D to stand for dimes, and Q for quarters.
Each dime is worth 10 cents, and each quarter is worth 25 cents.
The system is therefore
D+Q = 33 (total 33 coins)
10D+25Q=600 (total value of the coins)

Most of the time, this type of can be solved with only one equation, as follows:
D=number of dimes,
33-D=number of quarters, then for the total value
10D+25(33-D)=600
and solve for D.

Answer 2

Even better, this type of problems can be solved without algebra, as follows:
If all 33 coins are dimes, the total is worth is 825 cents.
We are short (in value) by 825-600=270 cents.
For each dime changed for a quarter, we increase the value by 25-10=15 cents.
Number of exchanges required = 270/15=18
So there are 18 quarters, (33-18)=15 dimes.

Answer 3

*If all 33 coins are dimes, the total is worth is 330 cents.
We are short (in value) by 600-330=270 cents.

Answer 4

Thank you so much I completely understood that!

Answer 5

You're welcome! :)