Peter has $4.80 in his piggy bank, consisting of dimes and quarters. If there are 33 coins in all, how many of each does he have?

10 quarters, 23 dimes

Step-by-step explanation:

Make dimes = d and quarters = q. Let the number of dimes and quarters add up to 33 and the value of the dimes and quarters add up to 4.80. The system of equations should look like:

d + q = 33 0.10d + 0.25q = 4.80

Solve for d in the first equation. Subtract q from both sides.

d = 33 - q

Substitute d into the second equation.

0.10 (33 - q) + 0.25q = 4.80

Distribute 0.10 inside the parentheses.

3.3 - 0.10q + 0.25q = 4.80

Combine like terms.

3.3 + 0.15q = 4.80

Subtract 3.3 from both sides.

0.15q = 1.5

Divide both sides by 0.15.

q = 10

Substitute this value of q into where we solved for d (d = 33 - q).

d = 33 - (10)

d = 23