Let's denote the price of a hot dog as \( h \) and the price of a cheeseburger as \( c \).
From the information given, we can set up a system of equations based on the orders of the two families.
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The Walker family ordered 4 hot dogs and 3 cheeseburgers for a total of $23.75: \[ 4h + 3c = 23.75 \quad \text{(Equation 1)} \]
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The Baldwin family ordered 6 hot dogs and 2 cheeseburgers for a total of $25: \[ 6h + 2c = 25 \quad \text{(Equation 2)} \]
Now we have the following system of equations: \[ \begin{align*} 4h + 3c &= 23.75 \quad \text{(1)} \ 6h + 2c &= 25 \quad \text{(2)} \end{align*} \]
To solve this system, we can use the method of substitution or elimination. Here, we'll use the elimination method.
First, let's multiply Equation 1 by 2 and Equation 2 by 3 to align the coefficients of \( c \): \[ \begin{align*} 8h + 6c &= 47.50 \quad \text{(Equation 3)} \ 18h + 6c &= 75 \quad \text{(Equation 4)} \end{align*} \]
Next, we can subtract Equation 3 from Equation 4: \[ (18h + 6c) - (8h + 6c) = 75 - 47.50 \] This simplifies to: \[ 10h = 27.50 \] Now, divide both sides by 10: \[ h = 2.75 \]
Now that we have the price of a hot dog \( h = 2.75 \), we can substitute this value back into either Equation 1 or Equation 2 to find the price of a cheeseburger \( c \). We'll use Equation 1: \[ 4(2.75) + 3c = 23.75 \] This simplifies to: \[ 11 + 3c = 23.75 \] Subtract 11 from both sides: \[ 3c = 12.75 \] Now, divide by 3: \[ c = 4.25 \]
Thus, the prices are:
- Price of a hot dog \( h = 2.75 \)
- Price of a cheeseburger \( c = 4.25 \)