Devi, Ethan and Farah sold some bookmarks at a school book fair. Each bookmark cost $4.60. Devi sold 14 of the bookmarks. Ethan and Farah sold the rest of the bookmarks in the ratio 4 : 5. Farah sold 90 more bookmarks than Devi.
- How many bookmarks did the three of them sell altogether?
- How much money did Ethan and Farah collect altogether?
Need a hint?
Make Devi's share and the rest into units of the same size. Devi's 14 is the same as 3 out of 12 equal units.
Worked answer
- (a) Make the whole 4 equal parts. Devi sold 1 part, so Ethan and Farah sold 3 parts.
- Split each of the 4 parts into 3 smaller units. The whole is 12 units. Devi sold 3 units, and Ethan and Farah sold 9 units.
- The ratio 4 : 5 has 4 + 5 = 9 parts, and 9 units are shared. So 1 part is 1 unit. Ethan sold 4 units and Farah sold 5 units.
- Farah sold 5 units and Devi sold 3 units. The difference is 5 − 3 = 2 units, and this is 90 bookmarks.
- 1 unit = 90 ÷ 2 = 45 bookmarks.
- Total = 12 × 45 = 540 bookmarks.
- (b) Ethan and Farah sold 9 units = 9 × 45 = 405 bookmarks.
- Money collected = 405 × $4.60 = $1863.
Answer: $1863
The mistake this question tests
Habit
Fraction of a remainder
Many pupils treat the ratio 4 : 5 as if it shared the whole amount, instead of only the 34 left after Devi. They forget that Devi's share must be in the same units as Ethan's and Farah's.
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See the answer →Practise PSLE ratio until the mistakes stop.
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