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

Question

quantity value total

nickels

quarters

together

Answer 1

To solve the problem, we can set up a system of equations based on the information provided.

Let \( n \) be the number of nickels and \( q \) be the number of quarters. We have the following information:

1. The total number of coins is 16.
2. The total value of the coins is $2, which is equivalent to 200 cents.

From this information, we can formulate our equations:

1. \( n + q = 16 \) (Equation 1: total number of coins)
2. \( 5n + 25q = 200 \) (Equation 2: total value of the coins in cents)

Now, we can simplify Equation 2 by dividing all terms by 5:

\[ n + 5q = 40 \] (Equation 3)

Now, we can solve the system of equations using Equation 1 and Equation 3.

Step 1: From Equation 1, express \( n \) in terms of \( q \):

\[ n = 16 - q \]

Step 2: Substitute \( n \) into Equation 3:

\[ (16 - q) + 5q = 40 \]

Step 3: Combine like terms:

\[ 16 + 4q = 40 \]

Step 4: Solve for \( q \):

\[ 4q = 40 - 16 \] \[ 4q = 24 \] \[ q = 6 \]

Step 5: Substitute back to find \( n \):

\[ n = 16 - q \] \[ n = 16 - 6 \] \[ n = 10 \]

Conclusion:

Sue received 10 nickels and 6 quarters.

To summarize the values:

| | quantity | value each | total value | |----------|----------|------------|-------------| | Nickels | 10 | 5 | 50 | | Quarters | 6 | 25 | 150 | | Together | 16 | | 200 |

Thus, the solution confirms that Sue has 10 nickels and 6 quarters for a total value of $2.