A farmer cuts a 300 feet fence into two pieces of different sizes. The longer piece is four times as long as the shorter piece. How long are the two pieces?
Answer: Shorter piece 60 feet, longer piece 240 feet.
Step-by-step solution
Given: Total length = 300 feet; Longer piece = 4 × shorter piece
To find: The lengths of the two pieces
To find: The lengths of the two pieces
Idea: Let the shorter piece be x; the longer is 4x. Together they make the whole fence.
- Let the shorter piece be x feet. Then the longer piece is 4x feet.1 mark
- x + 4x = 300, so 5x = 300.1 mark
- x = 60. Shorter piece = 60 feet; longer piece = 4 × 60 = 240 feet.1 mark
The pieces are 60 feet and 240 feet long.
Check: 60 + 240 = 300 ✓ and 240 = 4 × 60 ✓.
Answer to write in the exam
Let shorter piece = x feet; longer piece = 4x feet
x + 4x = 300 ⇒ 5x = 300 ⇒ x = 60
∴ The pieces are 60 feet and 240 feet long
Common mistakes that cost marks
- Writing 4x = 300 (forgetting the shorter piece) and getting 75 feet.
- Dividing 300 by 4 to get 75 and 225. The fence is split into 1 + 4 = 5 equal shares, not 4.
- Giving only x = 60 and not the longer piece.
How this can come in the exam
MCQ (1 mark)
A 120 m rope is cut into two pieces, one twice as long as the other. The longer piece is
- 60 m
- 40 m
- 80 m
- 90 m
Show answer
(C) 80 m
x + 2x = 120, so x = 40 and the longer piece is 80 m.
Short answer (3 marks)
A 210 cm ribbon is cut into two pieces so that one is 34 cm longer than the other. Find the lengths.
Show answer
Let the shorter be x; then x + (x + 34) = 210 (1 mark). 2x = 176, x = 88 (1 mark). The pieces are 88 cm and 122 cm (1 mark).Try one yourself
A 350 m wire is cut into two pieces; the longer is 6 times the shorter. Find both lengths.
Show answer
7x = 350, so x = 50. The pieces are 50 m and 300 m.
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