Question

Peter has been saving his loose change for several weeks. When he counted his quarters and dimes, he found they had a total value $18.30. The number of quarters was 12 more than three times the number of dimes. How many quarters and how many dimes did Peter have?

Answer 1

Let:

q be the number of quarters

d be the number of dimes

To solve this question, follow the steps below.

Step 01: Write an equation that relates the number of quarters and dimes.

Knowing that "The number of quarters was 12 more than three times the number of dimes":

$q=12+3\cdot d$

Step 02: Write an equation that shows the amount of money that Peter has.

Dime = 10 cents = $0.10.

Quarter = 25 cents = $0.25.

Then,

$0.1d+0.25q=18.30$

Step 03: Substitute q from step 1 in the equation from step 02.

$0.1d+0.25\cdot(12+3d)=18.30$

And solve the equation for d.

$\begin{gathered} 0.1d+0.25\cdot12+0.25\cdot3d=18.30 \\ 0.1d+3+0.75d=18.30 \\ 0.85d+3=18.30 \end{gathered}$

Subtracting 3 from both sides:

$\begin{gathered} 0.85d+3-3=18.30-3 \\ 0.85d=15.30 \end{gathered}$

And divide both sides by 0.85:

$\begin{gathered} \frac{0.85}{0.85}d=\frac{15.30}{0.85} \\ d=18 \end{gathered}$

The number of dimes is 18.

Step 04: Knowing the number of dimes, find the number of quarters.

$\begin{gathered} q=12+3\cdot d \\ q=12+3\cdot18 \\ q=66 \end{gathered}$

The number of quarters is 66.

In summary,

Number of dimes = 18.

Number of quarters = 66.