Question

the piggybank had $25.65 in dimes and quarters. If there were 20 more quarters than dimes, how many dimes were in the piggybank?

Answer 1

Let's define the number of dimes as \( d \) and the number of quarters as \( q \). According to the problem, we have the following information:

1. The total value of the dimes and quarters is $25.65, which can be expressed in cents as 2565 cents.
2. There are 20 more quarters than dimes, so we can express this relationship as:
\[
q = d + 20
\]

Now, we can express the total value in cents. The value of the dimes is \( 10d \) cents (since each dime is worth 10 cents), and the value of the quarters is \( 25q \) cents (since each quarter is worth 25 cents). Thus, we have the equation:
\[
10d + 25q = 2565
\]

Now we can substitute \( q \) from the first equation into this equation:
\[
10d + 25(d + 20) = 2565
\]

Expanding this:
\[
10d + 25d + 500 = 2565
\]
\[
35d + 500 = 2565
\]

Next, we solve for \( d \):
\[
35d = 2565 - 500
\]
\[
35d = 2065
\]
\[
d = \frac{2065}{35}
\]
\[
d = 59
\]

Now that we have the number of dimes, we can find the number of quarters:
\[
q = d + 20 = 59 + 20 = 79
\]

Thus, the number of dimes in the piggy bank is \( \boxed{59} \).