Solving systems

Question

During a Football game the parents of the devil football player so nachos and bags of popcorn to raise money for new uniforms. They charged $6.50 for nochez, and $4 for a bag of popcorn. The parents collect $723.50 in sales during the game. They sell a total of a 139 items. Set up a system of equations and solve to determine how many nachos and bags of popcorn were sold.

Answer 1

Hi Kryslin,

You can solve this problem by creating two equations and solving them using elimination to find the number of each item sold.

Let's use the variable, n , to represent the NUMBER of nachos sold and the variable, p , to represent the NUMBER of popcorn bags sold.

Since there was a total of 139 items sold, we can write the following equation to show this part of the situation: n + p = 139

Then using the item prices and the total amount of money taken in, we can write the following equation:

$6.50n + $4p = $723.50

Now we can solve these two equations simultaneously using elimination:

n + p = 139

6.50 n + 4 p = 723.50

Multiply the first equation by -6.50 and solve for p :

n + p = 139 becomes -6.50n + -6.50p = -903.50

-6.50n + -6.50p = -903.50

6.50n + 4 p = 723.50

-2.50p = -180

p = 72 bags if popcorn

Since there were 139 total items sold, n will be 67 nachos.

There were 72 bags of popcorn and 67 nachos sold.