Question

Rob has 40 coins, all dimes and quarters, worth $7.60. How many dimes and how many quarters does he have?

a
14 dimes and 26 quarters

b
16 dimes and 24 quarters

c
10 dimes and 30 quarters

Answer 1

Let \( d \) be the number of dimes and \( q \) be the number of quarters that Rob has. We know the following:

1. The total number of coins:
\[
d + q = 40
\]

2. The total value of the coins:
\[
0.10d + 0.25q = 7.60
\]

To eliminate the decimals, we can multiply the second equation by 100:
\[
10d + 25q = 760
\]

Now we have a system of linear equations:
1. \( d + q = 40 \)
2. \( 10d + 25q = 760 \)

We can solve the first equation for \( q \):
\[
q = 40 - d
\]

Now, substitute \( q \) into the second equation:
\[
10d + 25(40 - d) = 760
\]

Expanding this gives:
\[
10d + 1000 - 25d = 760
\]

Combine like terms:
\[
-15d + 1000 = 760
\]

Now, solve for \( d \):
\[
-15d = 760 - 1000
\]
\[
-15d = -240
\]
\[
d = \frac{-240}{-15} = 16
\]

Now substitute \( d \) back to find \( q \):
\[
q = 40 - d = 40 - 16 = 24
\]

Thus, Rob has \( 16 \) dimes and \( 24 \) quarters. The correct answer is:
**b 16 dimes and 24 quarters**.