Solving Systems of Equations Word Problems (4 methods)

Given a word problem you need to create 2 equations from the information and then solve the system of equations using one of your solving systems of equations methods.

1. Example:

At the WBL football game on Friday night there were a total of 500 tickets sold. They charged $7 for adult tickets and $5 for student tickets. The total revenue from ticket sales was $3100. How many adult and student tickets were sold?

Let x = Adults
Let y = Students

Pull out the important information from the paragraph:

Total tickets = 500
Total Revenue = $3100
Adult Cost = $7
Student Cost = $5

Using this information I created 2 equations; one showing total ticket sales and one showing total revenue.

x + y = 500
7x + 5y = 3100

(Remember when there is no number written in front of a variable there is an invisible 1)

Solving this problem using graphing method

Solving this problem using substitution

Solving this problem using linear combinations

Solving this problem using matrices

2. Example:

On opening night of a choir concert, 220 adult tickets and 100 children tickets were sold for a total revenue of $410. The next night 180 adult tickets and 120 children tickets were sold for a total revenue of $366. What is the price of an adult ticket and a child ticket?

Let x = adult tickets
Let y = child tickets

Using the information from the paragraph I created these equations:

220x + 100 y = 410
180x + 120y = 366

Solve using any of the 4 methods for solving systems of equations.

Solution Set : ($1.50, $0.80)