Question

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?

Answer 1

Step- 1: Find the total price of a hot dog and cold drinks Jamie buys:

let the price of hot dogs be $\mathrm{H}$ and the price of soft drinks be $\mathrm{D}$.

Given that Jamie buys $6$ hot dogs, $4$soft drinks for $\$13$.

So the price of $6$ hot dogs is $6\mathrm{H}$ and the price of $4$soft drinks is $4\mathrm{D}$.

Total price of hot dogs and soft drinks Jamie buys is $6\mathrm{H}+4\mathrm{D}=13$.

Step- 2: Find the total price of a hot dog and cold drinks Amy buys:

Given that Amy buys $3$hot dogs,, $4$soft drinks for $\$8.50$.

So the price of $3$ hot dogs is $3\mathrm{H}$ and the price of $4$soft drinks is $4\mathrm{D}$.

Total price of hot dogs and soft drinks Amy buys is $3\mathrm{H}+4\mathrm{D}=8.50$.

Step- 3: Find the price of a hot dog:

Two algebraic equation are obtained above as:

$6\mathrm{H}+4\mathrm{D}=13...\left(1\right)$.

$3\mathrm{H}+4\mathrm{D}=8.50...\left(2\right)$.

Subtract equation $\left(2\right)$ from equation $\left(1\right)$:

$$\begin{gathered} 6\mathrm{H}+4\mathrm{D}-(3\mathrm{H}+4\mathrm{D})=13-8.50 \\ 6\mathrm{H}+4\mathrm{D}-3\mathrm{H}-4\mathrm{D}=4.50 \\ 3\mathrm{H}-0=4.50 \\ 3\mathrm{H}=4.50 \\ \mathrm{H}=\frac{4.50}{3} \\ \mathrm{H}=1.50 \end{gathered}$$

Therefore the price of a hot dog is $\$1.50$.