Hana placed two strips of paper, M and N, so that they overlap. The overlapping part is 25 of strip M and also 14 of strip N. Strip N is 18 cm longer than strip M. What is the length of strip M?
Need a hint?
Write the overlap as 2 units. Then find how many units make all of M and all of N, and use the 18 cm difference to find one unit.
Worked answer
- The overlap is 25 of M, so split M into 5 equal units; the overlap is 2 units.
- The overlap is 14 of N, so N is 4 times the overlap: N = 4 × 2 = 8 units.
- N − M = 8 units − 5 units = 3 units.
- 3 units = 18 cm, so 1 unit = 6 cm.
- M = 5 units = 5 × 6 cm = 30 cm.
The mistake this question tests
Stopped at one part in ratio
Pupils often take the overlap length as the answer, or treat the 18 cm difference as the length of M, without first building the full length of each strip from its fraction.
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