Question

The Walker and Baldwin families ordered lunch at the refreshment stand at the basketball game. The Walker family ordered 4 hot dogs and 3 cheeseburgers and paid $23.75. The Baldwin family ordered 6 hots dogs and 2 cheeseburgers and paid $25. Write a system of equations using h for hot dogs and c for cheeseburgers.(1 point) Responses 4h + 3c = 23.75 and 6h + 2c = 25 4h + 3c = 23.75 and 6h + 2c = 25 h + c = 23.75 and h + c = 25 h + c = 23.75 and h + c = 25 4h − 3c = 23.75 and 6h − 2c = 25 4h − 3c = 23.75 and 6h − 2c = 25 7c = 23.75 and 8h = 25 7c = 23.75 and 8h = 25 Question 2 What are the prices of a hot dog and a cheeseburger? This question requires you to show your work. (2 points) $4.25 $2.00 $5.00 $2.75 hot dog cheeseburger

Answer 1

To create a system of equations based on the lunch orders from the Walker and Baldwin families, we will let \( h \) represent the price of a hot dog and \( c \) represent the price of a cheeseburger.

1. **Walker Family Order:**
- They ordered 4 hot dogs and 3 cheeseburgers for a total of $23.75.
- This gives us the equation:
\[
4h + 3c = 23.75
\]

2. **Baldwin Family Order:**
- They ordered 6 hot dogs and 2 cheeseburgers for a total of $25.
- This gives us the equation:
\[
6h + 2c = 25
\]

Thus, the system of equations is:
\[
\begin{align*}
1) & \quad 4h + 3c = 23.75 \\
2) & \quad 6h + 2c = 25
\end{align*}
\]

Next, we will solve this system of equations.

### Step 1: Solve one equation for one variable

Let's solve the second equation for \( c \):

From equation 2:
\[
6h + 2c = 25
\]
Subtract \( 6h \) from both sides:
\[
2c = 25 - 6h
\]
Now, divide by 2:
\[
c = \frac{25 - 6h}{2}
\]

### Step 2: Substitute into the first equation

Now, we substitute \( c \) into the first equation \( 4h + 3c = 23.75 \):

\[
4h + 3\left(\frac{25 - 6h}{2}\right) = 23.75
\]

Clear the parentheses:
\[
4h + \frac{75 - 18h}{2} = 23.75
\]

Multiply the entire equation by 2 to eliminate the fraction:
\[
8h + (75 - 18h) = 47.5
\]

Combine like terms:
\[
8h - 18h + 75 = 47.5
\]

This simplifies to:
\[
-10h + 75 = 47.5
\]

### Step 3: Isolate \( h \)

Subtract 75 from both sides:
\[
-10h = 47.5 - 75
\]
\[
-10h = -27.5
\]

Now, divide by -10:
\[
h = 2.75
\]

### Step 4: Substitute back to find \( c \)

Now, substitute \( h = 2.75 \) back into the equation we derived for \( c \):
\[
c = \frac{25 - 6(2.75)}{2}
\]
Calculating \( 6(2.75) \):
\[
6(2.75) = 16.5
\]
Now substitute:
\[
c = \frac{25 - 16.5}{2}
\]
\[
c = \frac{8.5}{2} = 4.25
\]

### Conclusion

The prices are:
- Hot Dog \( h = 2.75 \)
- Cheeseburger \( c = 4.25 \)

Final answer:
- Hot Dog: **$2.75**
- Cheeseburger: **$4.25**