Mei laid two ribbons, X and Y, side by side. The overlapping part is 25 of ribbon X and also 13 of ribbon Y. Ribbon Y is 10 cm longer than ribbon X. What is the length of ribbon Y?
Need a hint?
Write the overlap two ways, once as a fraction of X and once as a fraction of Y. Then find how much longer Y is than X in fifths of X.
Worked answer
- The overlap is the same length, so 25 of X = 13 of Y.
- Then Y = 65 of X, because 13 of Y is 25 of X and 25 ÷ 13 = 65.
- Y is 65 of X, so the extra length Y − X is 15 of X.
- 15 of X = 10 cm, so X = 50 cm.
- Y = 50 + 10 = 60 cm. Check: 25 of 50 = 20 and 13 of 60 = 20.
The mistake this question tests
Stopped at one part in ratio
Pupils often turn the ratio round to X : Y = 6 : 5 and give 50 cm, which is the length of ribbon X, not ribbon Y.
How to fix it at home →Wrong answers children often give:
- 50 Stopped at one part in ratio
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