A toy store had yo-yos and kites in the ratio 5 : 3 at first. The store sold 15 yo-yos and received 27 more kites. After this, the ratio of the number of yo-yos to the number of kites became 2 : 3. How many kites were there at first?
Need a hint?
Write the yo-yos and kites at first as units, then write both amounts after the change and use the new ratio 2 : 3 to find one unit.
Worked answer
- Let 1 unit be the number of yo-yos divided by 5 at first, so yo-yos at first = 5 units and kites at first = 3 units.
- After the sale, yo-yos = 5 units - 15 and kites = 3 units + 27.
- Set (5 units - 15) : (3 units + 27) = 2 : 3, so 3 (5 units - 15) = 2 (3 units + 27).
- 15 units - 45 = 6 units + 54, so 9 units = 99 and 1 unit = 11.
- Kites at first = 3 × 11 = 33.
Answer: 33 kites
The mistake this question tests
Habit
Stopped at one part in ratio
Pupils add the 27 kites to the ratio number directly, or they treat the 15 yo-yos sold as added, which breaks the before-and-after relationship.
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See the answer →Practise PSLE ratio until the mistakes stop.
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