Hao, Priya and Siti sold some raffle tickets at a school carnival. Each ticket cost $3.50. Hao sold 13 of the tickets. Priya and Siti sold the rest of the tickets in the ratio 7 : 2. Priya sold 40 more tickets than Hao.
- How many tickets did the three of them sell altogether?
- How much more money did Priya collect than Siti?
Need a hint?
Give the whole amount 27 units so that Hao's 13 is a whole number of units. Find the units for Priya and Siti from the remainder.
Worked answer
- (a) Hao sold 13, so the rest is 23. The rest is shared in the ratio 7 : 2, which is 9 parts. Make the whole 27 units, so each third is 9 units and Hao sold 9 units.
- The rest is 23 of the total = 2 × 9 = 18 units.
- Priya and Siti share 18 units in the ratio 7 : 2. Since 7 + 2 = 9 parts, each part = 18 ÷ 9 = 2 units. Priya = 7 × 2 = 14 units, Siti = 2 × 2 = 4 units.
- Priya − Hao = 14 − 9 = 5 units, and this is 40 tickets. 1 unit = 40 ÷ 5 = 8 tickets.
- Total = 27 units = 27 × 8 = 216 tickets.
- (b) Priya − Siti = 14 − 4 = 10 units = 10 × 8 = 80 tickets.
- Money = 80 × $3.50 = $280.
Answer: $280
The mistake this question tests
Habit
Fraction of a remainder
Many pupils split the whole in the ratio 7 : 2 instead of only the rest after Hao's share, or they forget to multiply the ticket difference by the price in part (b).
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