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CLASS 8 MATHS · LINEAR EQUATIONS IN ONE VARIABLE

Linear equation word problems

Let the unknown be x, write the story as an equation, then solve it step by step.

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Worked examples

Example 1 · level 1

A rectangular park in Indore is 7 m longer than it is wide. Its perimeter is 126 m. What is its breadth (in m)?

Show solution
  1. Breadth = x, length = x + 7.
  2. 2(x + 7 + x) = 126 → 4x + 14 = 126.
  3. 4x = 112 → x = 28 m. (Length = 35 m.)

Answer: 28 m

Example 2 · level 2

The sum of 3 consecutive whole numbers is 39. What is the smallest of them?

Show solution
  1. Let the smallest be x: x + (x + 1) + (x + 2) = 39.
  2. 3x + 3 = 39 → 3x = 36.
  3. x = 36 ÷ 3 = 12. The numbers are 12, 13 and 14.

Answer: 12

Example 3 · level 3

Isha's piggy bank has 45 coins, all ₹2 and ₹5 coins, worth ₹102 in total. How many ₹5 coins are there?

Show solution
  1. ₹5 coins = x, ₹2 coins = 45 − x.
  2. 5x + 2(45 − x) = 102 → 3x + 90 = 102.
  3. 3x = 12 → x = 4. (41 coins of ₹2.)

Answer: 4

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