Question

At a baseball game, a vender sold a combined total of 208 sodas and hotdogs. The number of hot dogs sold was 42 less than the number of sodassold. Find the number of sodas sold and the number of hot dogs sold.

Answer 1

Let x be the number of sodas sold

Lef y be the number of hot dogs sold

At a baseball game, a vender sold a combined total of 208 sodas and hot dogs:

$x+y=208$

The number of hot dogs sold was 42 less than the number of sodas sold:

$y=x-42$

Use the next system of equations to solve the question:

$\begin{gathered} x+y=208 \\ y=x-42 \end{gathered}$

1- Use the second equation in the frist equation:

$x+(x-42)=208$

2- Solve x.

$\begin{gathered} x+x-42=208 \\ 2x-42=208 \\ \\ \text{Add 42 in both sides of the equation:} \\ 2x-42+42=208+42 \\ 2x=250 \\ \\ \text{Divide both sides of the equation into 2:} \\ \frac{2}{2}x=\frac{250}{2} \\ \\ x=125 \end{gathered}$

3- Use the value of x to solve y:

$\begin{gathered} y=x-42 \\ y=125-42 \\ \\ y=83 \end{gathered}$

Then, the number of sodas sold was 125 and the number of hot dogs sold was 83