Linear Equation Applications
Linear equations model real-world situations. Setting up and solving equations from word problems is a key skill in Year 8 algebra, connecting maths to everyday contexts.
What You Need to Know
Key Concept Diagram
Define a variable to represent the unknown quantity in the problem
Write an equation that models the relationship described
Solve the equation using inverse operations, maintaining balance
Check your answer makes sense in the original context
Key Vocabulary
Variable
A letter representing an unknown or changing quantity
Equation
A mathematical statement that two expressions are equal
Inverse operation
The operation that undoes another (e.g. subtraction undoes addition)
Coefficient
The number multiplied by a variable in a term
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
A plumber charges $60 call-out fee plus $45 per hour. The total bill was $195. How many hours did the plumber work?
Question 2
Two numbers add to 50 and one is three times the other. What is the smaller number?
Question 3
Maria bought 5 identical books and spent $12.50 on a bookmark. She spent $87.50 in total. What was the price of each book?
Key Concepts Summary
- ●Define a variable to represent the unknown quantity in the problem
- ●Write an equation that models the relationship described
- ●Solve the equation using inverse operations, maintaining balance
- ●Check your answer makes sense in the original context