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?

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.