Question

Sue bought a chocolate bar and received change for $2 in 16 coins, all nickels and quarters, how many of each kind are given?

Answer 1

Let \( n \) be the number of nickels and \( q \) be the number of quarters. We know two things from the problem statement:

1. The total number of coins is 16:
\[
n + q = 16
\]

2. The total amount of change is $2, which is 200 cents. The value of the nickels and quarters can be expressed in cents:
\[
5n + 25q = 200
\]

Now we have a system of equations:

1. \( n + q = 16 \)
2. \( 5n + 25q = 200 \)

We can simplify the second equation by dividing everything by 5:
\[
n + 5q = 40
\]

Now we can solve the system of equations:
From the first equation, we can express \( n \) in terms of \( q \):
\[
n = 16 - q
\]

Substituting \( n \) into the simplified second equation:
\[
(16 - q) + 5q = 40
\]
\[
16 - q + 5q = 40
\]
\[
16 + 4q = 40
\]
\[
4q = 40 - 16
\]
\[
4q = 24
\]
\[
q = 6
\]

Now we can find \( n \):
\[
n = 16 - q = 16 - 6 = 10
\]

So, Sue received 10 nickels and 6 quarters.

Thus, the solution is:
- Nickels: 10
- Quarters: 6