Systems of Equations Word Problems

** Important Note:  Before completing this unit, you must first be thoroughly comfortable with how to solve systems of equations, systems of inequalities, and linear word problems.  If you are not completely comfortable you need to go back to those units, and review until you are.  This unit is a more advanced topic that requires mastery of the basics first. **

How to identify a system of equations word problem

Look for two things being compared in two ways. Some examples may help:

The admission fee at a small fair is $1.50 for children and $4.00 for adults. On a certain day, 2200 people enter the fair and $5050 is collected. How many children and how many adults attended?

This is comparing adult tickets and child tickets in two ways: the amount of tickets and the money they generated.

The sum of the digits of a two-digit number is 7. When the digits are reversed, the number is increased by 27. Find the number.

This is comparing the digits of a two-digit number in two ways: the sum of them and what occurs when they’re reversed.

A landscaping company placed two orders with a nursery. The first order was for 13 bushes and 4 trees, and totaled $487. The second order was for 6 bushes and 2 trees, and totaled $232. The bills do not list the per-item price. What were the costs of one bush and of one tree?

This is comparing two orders of bushes and trees in two ways: how much one order cost and how much a second order cost.

Strategy:

  1. Identify the two things being compared and assign variable letters to them (Use letters that can easily be kept straight: If comparing apples and bananas, use and b).
  2. Set up your first and second equations.
  3. Use substitution or combination/elimination to solve.