Question

rosalyn's company, snack attack inc., owns a few vending machines. Last night she collected $82.50 in dimes and quarters. If rosalyn collected 50 more quarters than dimes, how many dimes did she collect?

Answer 1

Let \( d \) represent the number of dimes Rosalyn collected. According to the problem, the number of quarters she collected is \( d + 50 \).

The value of the dimes collected is \( 0.10d \) dollars, and the value of the quarters collected is \( 0.25(d + 50) \) dollars.

The total amount collected is given as $82.50. So we can write the equation:

\[
0.10d + 0.25(d + 50) = 82.50
\]

Now, let's simplify the equation:

\[
0.10d + 0.25d + 0.25 \times 50 = 82.50
\]

Calculating \( 0.25 \times 50 \):

\[
0.25 \times 50 = 12.50
\]

So the equation now becomes:

\[
0.10d + 0.25d + 12.50 = 82.50
\]

Combining the \( d \) terms:

\[
0.35d + 12.50 = 82.50
\]

Now, subtract \( 12.50 \) from both sides:

\[
0.35d = 82.50 - 12.50
\]
\[
0.35d = 70.00
\]

Now, divide both sides by \( 0.35 \):

\[
d = \frac{70.00}{0.35}
\]
\[
d = 200
\]

Thus, Rosalyn collected \( \boxed{200} \) dimes.

To confirm, we can calculate the number of quarters:

\[
d + 50 = 200 + 50 = 250
\]

Now, calculating the total amount collected:

Value of dimes:

\[
200 \times 0.10 = 20.00 \text{ dollars}
\]

Value of quarters:

\[
250 \times 0.25 = 62.50 \text{ dollars}
\]

Adding both values together:

\[
20.00 + 62.50 = 82.50 \text{ dollars}
\]

This matches the amount collected, confirming that the solution is correct. Rosalyn collected \( \boxed{200} \) dimes.