Systems of Linear Equations Word Problems: Foundations

[Video Placeholder - Solving word problems with systems]

Duration: 6:45

Approach to Systems Word Problems

When solving word problems that require systems of equations:

  1. Identify the two unknowns (usually what the question asks about)
  2. Define variables for these unknowns
  3. Translate the given information into two equations
  4. Solve the system using substitution, elimination, or graphing
  5. Interpret the solution in the context of the problem

Example 1: Cost Problem

A movie theater charges $8 for adults and $5 for children. On a particular day, the theater sold 120 tickets and made $840. How many adult tickets were sold?

Example 2: Mixture Problem

A chemist needs to make 100 ml of a 16% acid solution. She has 10% and 20% solutions available. How much of each should she mix?

Try it!

A sports store sells basketballs for $20 each and soccer balls for $15 each. Yesterday the store sold 50 balls total and made $850. How many basketballs were sold?

Step 1: Define variables

Let b =

Let s =

Step 2: Write the system of equations

(Total balls)

(Total revenue)

Step 3: How many basketballs were sold?

Common Problem Types

Example 3: Rate Problem

Two cars start from the same point and travel in opposite directions. One travels at 60 mph and the other at 45 mph. In how many hours will they be 420 miles apart?

Example 4: Number Problem

The sum of two numbers is 72. Their difference is 16. What are the numbers?

Practice: Identify the Equations

A school is selling tickets to a play. Student tickets cost $3 and adult tickets cost $5. The school sold 150 tickets and collected $590. Which system represents this situation?