At first, Farah had a total of 185 yellow and turquoise cards, while her friend had no cards. After Farah gave 25 yellow cards and 20% of her turquoise cards to her friend, the ratio of the number of yellow cards to the number of turquoise cards she had left was 3 : 4.
- How many yellow cards did Farah have at first?
- After her friend used some yellow cards and some turquoise cards, the ratio of the number of yellow cards to the number of turquoise cards that her friend had left became 4 : 7. What was the least number of turquoise cards that her friend could have used?
Need a hint?
Use a bar model for the 3 : 4 ratio and remember that 80% remained. For part (b), express the final ratio as 4v : 7v and test the greatest whole-number value of v that fits the friend's cards.
Worked answer
- (a) Let the yellow and turquoise cards left be 3u and 4u.
- Since 80% of the original turquoise cards remained, the original number was 4u ÷ 80% = 5u.
- Farah originally had 3u + 25 yellow cards, so 5u + 3u + 25 = 185.
- 8u = 160, so u = 20. Farah had 3 × 20 + 25 = 85 yellow cards and 5 × 20 = 100 turquoise cards at first.
- Farah gave her friend 20% of 100 = 20 turquoise cards, so her friend had 25 yellow cards and 20 turquoise cards.
- (b) Write the friend's cards left as 4v : 7v. Some turquoise cards were used, so 7v is less than 20. The greatest whole number v is 2 (7 × 2 = 14, but 7 × 3 = 21).
- With v = 2, the friend had 8 yellow and 14 turquoise cards left. She used 25 − 8 = 17 yellow and 20 − 14 = 6 turquoise cards, so the least number of turquoise cards used is 6.
The mistake this question tests
Stopped at one part in ratio
Some pupils take v = 1 (4 yellow and 7 turquoise left) and answer 20 − 7 = 13. To use the fewest turquoise cards, keep as many as possible, so take the greatest v that fits.
How to fix it at home →Wrong answers children often give:
- 13 Stopped at one part in ratio
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See the answer →Practise PSLE ratio until the mistakes stop.
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