afton has fourteen dollars and ninety five cents worth of quarters and dimes. If afton has four times as many dimes as she does quarters, how many quarters does she have?

1 answer

Let the number of quarters be \( q \). Since Afton has four times as many dimes as quarters, the number of dimes is \( 4q \).

Next, we calculate the total value of the quarters and dimes:

  • The value of the quarters is given by \( 0.25q \) (since each quarter is worth 25 cents).
  • The value of the dimes is given by \( 0.10(4q) = 0.40q \) (since each dime is worth 10 cents).

We can sum these values to find the total value that Afton has:

\[ 0.25q + 0.40q = 14.95 \]

Combining the terms gives:

\[ 0.65q = 14.95 \]

To find \( q \), we divide both sides by 0.65:

\[ q = \frac{14.95}{0.65} \]

Now let's calculate it:

\[ q = \frac{14.95 \times 100}{65} = \frac{1495}{65} = 23 \]

So, Afton has \( \boxed{23} \) quarters.

To verify, we can calculate the number of dimes:

\[ 4q = 4 \times 23 = 92 \]

Now, let's check the total value:

  • Value of quarters: \( 23 \times 0.25 = 5.75 \) dollars
  • Value of dimes: \( 92 \times 0.10 = 9.20 \) dollars

Adding these two amounts together:

\[ 5.75 + 9.20 = 14.95 \text{ dollars} \]

The calculation is correct, confirming that Afton has \( \boxed{23} \) quarters.