Question

ed, the pay phone repair man, has $12,75 in dimes and quarters. If Ed has 30 more quarters than dimes, how many dimes does he have?

Answer 1

Let the number of dimes Ed has be \( d \). Since Ed has 30 more quarters than dimes, the number of quarters he has can be expressed as \( d + 30 \).

Next, we need to write the total value of the dimes and quarters in terms of dollars. The value of the dimes in dollars is given by:

\[
0.10d
\]

The value of the quarters in dollars is given by:

\[
0.25(d + 30)
\]

According to the problem, the total amount of money Ed has is $12.75. Therefore, we can set up the equation:

\[
0.10d + 0.25(d + 30) = 12.75
\]

Now, we will expand and simplify this equation:

\[
0.10d + 0.25d + 0.25 \times 30 = 12.75
\]

Calculating \( 0.25 \times 30 \):

\[
0.25 \times 30 = 7.50
\]

Now substitute that back into the equation:

\[
0.10d + 0.25d + 7.50 = 12.75
\]

Combining the \( d \) terms:

\[
0.35d + 7.50 = 12.75
\]

Next, we subtract 7.50 from both sides:

\[
0.35d = 12.75 - 7.50
\]

Calculating the right-hand side:

\[
12.75 - 7.50 = 5.25
\]

So now we have:

\[
0.35d = 5.25
\]

To find \( d \), divide both sides by 0.35:

\[
d = \frac{5.25}{0.35}
\]

Calculating the division:

\[
d = 15
\]

Thus, Ed has \( \boxed{15} \) dimes.

To verify, we calculate the number of quarters:

The number of quarters is:

\[
d + 30 = 15 + 30 = 45
\]

Calculating the total value:

The value of 15 dimes is:

\[
15 \times 0.10 = 1.50
\]

The value of 45 quarters is:

\[
45 \times 0.25 = 11.25
\]

Adding both values:

\[
1.50 + 11.25 = 12.75
\]

The calculations confirm that the total is indeed $12.75, verifying our solution that Ed has \( \boxed{15} \) dimes.