Solve linear equations: word problems

key notes :

Understand What a Word Problem Is

  • A word problem describes a real-life situation using words.
  • Your job is to translate those words into a mathematical equation.

Identify the Unknown

  • Decide what you’re solving for (usually labeled as x).
  • Example: “A number increased by 5 is 12” → Let the number be x.

Translate Words into Algebraic Expressions

Keywords and their meanings:

  • Sum / increased by / more than → Addition
  • Difference / decreased by / less than → Subtraction
  • Product / times → Multiplication
  • Quotient / divided by → Division
  • Equals / is / results in → =

Write the Linear Equation

  • Based on the expressions from the word problem.
  • Example: “Twice a number decreased by 4 is 10” →
    → 2x−4=102

Solve the Equation

Use inverse operations to isolate the variable (x).

Steps:

  • Simplify both sides.
  • Add or subtract terms.
  • Multiply or divide to find the value of x.

Check Your Solution

  • Plug your value of x back into the original word problem.
  • Make sure it makes sense in the real-world context.

Common Types of Word Problems

  • Age problems
  • Number problems
  • Money problems
  • Distance = Speed × Time problems
  • Geometry problems (perimeter, area)

Learn with an example

Gina learns 3 new starter recipes during each week of culinary school. After 14 weeks of culinary school , how many total starter recipes will Gina know?

_______starter recipes.

Write an equation that shows the relationship between the number of weeks Gina attends culinary school and the number of starter recipes she knows a. Then solve.

a=3 . 14

a=42 multiply

After 14 weeks of culinary school, Gina will know a total of 42 starter recipes.

Bridget has already written 2 pages ,and she expects to write 1 page for every additional hour spent writing. After spending 45 hours writing this week, how many pages will Bridget have written in total?

_______pages

Write an equation that shows the relationship between the amount of time spent writing and number of pages written p. Then solve.

p = 1 · 45 + 2

p = 45 + 2 Multiply

p = 47 Add

After spending 45 hours writing this week, Bridget will have written a total of 47 pages.

Valentina walks 3 kilometres during each trip to school. After 6 trips to school, how many kilometres will Valentina have walked in total? 

_______kilometres.

Write an equation that shows the relationship between the number of trips to school and the total distance walked d. Then solve.

d = 3 · 6

d = 18 Multiply

After 6 trips to school ,Valentina will have walked 18 kilometres.

Let’s practice!