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Word Problems as Equations

Turn a real situation into an equation, solve it, then check the answer makes sense.

Turning Words into Equations

Word problems follow three steps: 1 Choose a letter for the unknown number and say what it means. 2 Write an equation that matches the words exactly. 3 Solve the equation, then check the answer against the original question.

Example 1 — easy numbers

A number, plus 7, is 20 . Find the number. 1 Let the number be x . 2 Write the equation: x + 7 = 20 3 Solve: x = 13 Check: 13 + 7 = 20 ✓ Answer: 13

Example 2 — a rate problem

A taxi charges a fixed 3 pl u s 2 for every kilometre. A ride costs $17. How many kilometres was the ride? 1 Let the number of kilometres be x . 2 Write the equation: 2 x + 3 = 17 3 Solve: 2 x = 14, so x = 7 Check: 2 (7) + 3 = 14 + 3 = 17 ✓ Answer: 7 kilometres

Example 3 — two unknowns linked by one letter

A father is 3 times as old as his son. Together their ages add up to 48 . How old is the son? 1 Let the son's age be x . The father's age is 3 x . 2 Write the equation: x + 3 x = 48 3 Solve: 4 x = 48, so x = 12 Check: son 12, father 36, total 48 ✓ Answer: The son is 12 years old.

Example 4 — consecutive numbers

Three consecutive numbers add up to 36 . Find the smallest number. 1 Let the smallest number be x . The next two are x + 1 and x + 2 . 2 Write the equation: x + (x + 1) + (x + 2) = 36 3 Simplify: 3 x + 3 = 36 4 Solve: 3 x = 33, so x = 11 Check: 11 + 12 + 13 = 36 ✓ Answer: 11

Practice

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A number multiplied by 4, then increased by 5, gives 33 . Which equation matches this?

A rectangle's length is twice its width. Its perimeter is 30 cm. What is the width, in cm? (Perimeter = 2 \times length + 2 \times width.)

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