Question

This system of equations represents Reese’s pocket change. Let n represent the number of nickels and d represent the number of dimes Reese has in his pocket.

n + d = 11

5n + 10d = 70

How many dimes are in Reese’s pocket?

Answer 1

To solve the system of equations, we have:

1. \( n + d = 11 \) (1)
2. \( 5n + 10d = 70 \) (2)

We can simplify equation (2) by dividing everything by 5:

\[
n + 2d = 14 \quad \text{(3)}
\]

Now we have a new system of equations to work with:

1. \( n + d = 11 \) (1)
2. \( n + 2d = 14 \) (3)

Next, we can subtract equation (1) from equation (3):

\[
(n + 2d) - (n + d) = 14 - 11
\]

This simplifies to:

\[
d = 3
\]

Now that we have the value of \( d \), we can substitute it back into equation (1) to find \( n \):

\[
n + 3 = 11
\]
\[
n = 11 - 3
\]
\[
n = 8
\]

Thus, the number of dimes \( d \) in Reese's pocket is \( \boxed{3} \).