Devi bought some ribbon and cut it into long pieces and short pieces for gift boxes. The 4 long pieces and 3 short pieces she cut first used 4 m 80 cm of the ribbon. The ribbon that was left was not enough for another long piece, as it was short by 30 cm. Instead, she cut one more short piece and had 20 cm of ribbon left over.
- How much longer is a long piece than a short piece? (1 mark)
- How many metres of ribbon did Devi buy at first? (2 marks)
Need a hint?
The ribbon left over is the same amount whether you compare it with a long piece or a short piece. Use that to find how much longer a long piece is.
Worked answer
- (a) The ribbon left = 1 long piece − 30 cm.
- The same ribbon left = 1 short piece + 20 cm.
- So 1 long piece − 30 cm = 1 short piece + 20 cm.
- A long piece is 30 + 20 = 50 cm longer than a short piece.
- (b) 4 long pieces + 3 short pieces = 7 short pieces + 4 × 50 cm = 7 short pieces + 200 cm.
- 4 m 80 cm = 480 cm, so 7 short pieces = 480 − 200 = 280 cm.
- 1 short piece = 280 ÷ 7 = 40 cm, so 1 long piece = 40 + 50 = 90 cm.
- Ribbon left = 40 + 20 = 60 cm (check: 90 − 30 = 60).
- Ribbon bought = 480 + 60 = 540 cm = 5.4 m.
The mistake this question tests
Converting units (kg, ℓ, m, cm³)
Many pupils stop at 4 m 80 cm, forgetting that the ribbon left over was also part of what she bought. Others add the 30 cm instead of finding the difference between the two pieces.
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