A toy shop had yo-yos and kites in the ratio 3 : 4 at first. The shop sold 6 yo-yos and received 18 more kites. After this, the ratio of the number of yo-yos to the number of kites became 1 : 2. How many toys were there altogether in the end?
Need a hint?
Write the ratio after the changes as 1 : 2, then find the value of one unit before finding the total.
Worked answer
- Draw the ratio: after the changes, kites = 2 units and yo-yos = 1 unit.
- Yo-yos after = 3u − 6 and kites after = 4u + 18, so 4u + 18 = 2 × (3u − 6).
- 4u + 18 = 6u − 12, so 2u = 30 and u = 15.
- Yo-yos in the end = 3 × 15 − 6 = 39 and kites in the end = 4 × 15 + 18 = 78.
- Total in the end = 39 + 78 = 117.
Answer: 117 toys
The mistake this question tests
Habit
Stopped at one part in ratio
Many pupils add the changes to the original ratio: they keep the kites at 60 (forgetting the 18 added) or find the total at first (105) and stop there.
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See the answer →Practise PSLE ratio until the mistakes stop.
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