At a high school football game Jamie buys 6 hot dogs and 4 soft drinks for $13. Amy buys 3 hot dogs and 4 soft drinks for $8.50. What is the price of a hot dog?

Question

Responses
A $0.75$0.75
B $1.00$1.00
C $1.25$1.25
D $1.50

Answer 1

Let's denote the price of a hot dog as \( h \) and the price of a soft drink as \( d \).

From the information given, we can set up the following equations based on the purchases:

1. For Jamie: \[ 6h + 4d = 13 \]

2. For Amy: \[ 3h + 4d = 8.50 \]

Now, we have a system of equations:

\[ \begin{align*} 6h + 4d & = 13 \quad \text{(1)} \ 3h + 4d & = 8.50 \quad \text{(2)} \end{align*} \]

To eliminate \( d \), we can subtract equation (2) from equation (1):

\[ (6h + 4d) - (3h + 4d) = 13 - 8.50 \]

This simplifies to:

\[ 3h = 4.50 \]

Now, we can solve for \( h \):

\[ h = \frac{4.50}{3} = 1.50 \]

So, the price of a hot dog is \( \boxed{1.50} \).