Question

question
stella has $4.50 worth of dimes and quarters. she has 3 more dimes than quarters. determine the number of dimes and the number of quarters that stella has.
answer attempt 1 out of 2
there are
dimes and
quarters.
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Explanation:

Step1: Define variables

Let \( q \) be the number of quarters, then the number of dimes is \( q + 3 \).

Step2: Set up the equation

The value of a quarter is \( \$0.25 \) and a dime is \( \$0.10 \). The total value is \( \$4.50 \), so:
\( 0.25q + 0.10(q + 3) = 4.50 \)

Step3: Solve the equation

First, expand the left side:
\( 0.25q + 0.10q + 0.30 = 4.50 \)
Combine like terms:
\( 0.35q + 0.30 = 4.50 \)
Subtract \( 0.30 \) from both sides:
\( 0.35q = 4.50 - 0.30 = 4.20 \)
Divide both sides by \( 0.35 \):
\( q = \frac{4.20}{0.35} = 12 \)

Step4: Find the number of dimes

The number of dimes is \( q + 3 = 12 + 3 = 15 \)

Answer:

There are \( \boldsymbol{15} \) dimes and \( \boldsymbol{12} \) quarters.