Question

Luke and Leia are selling hot dogs and hamburgers at a minor league baseball game. At the end of the day they determine they have sold a total of 45 items and earned $195. If hot dogs cost $4 and hamburgers cost $5, how many did they sell of each?

What would be a system of equations for the scenario above?

Answer 1

15 hamburgers were sold and 30 hotdogs were sold.

The systems of equations are x + y = 45 and 4x + 5y = 195.

Explanation:

Let's make two equations.

x + y = 45

This represents the total of hotdogs and hamburgers sold

4x + 5y = 195

This represents the amount of money made for each food.

These are systems of equations, when you use 2 equations to solve a problem. I will use the strategy, Elimination for the following systems of equations. Anyways the goal is to multiply a number to x + y = 45 to cancel out one of the variables in 4x + 5y = 195. In other words, when we add these equations, the sum of the xs or ys will equal 0.

Let's multiply -5 to both x and y.

Now we have -5x -5y = -225 + 4x + 5y= 195

We will end up with -x = -30. This means that x = 30.

Now that we know x = 30, we can plug in 30 as x in one of the equations. I will plug in 30 into x + y = 45. 30 + y = 45.

Solve for y in 30 + y = 45, so y=15.

This means 15 hamburgers were sold and 30 hotdogs were sold.