Ravi prepared red and blue felt badges for a school charity booth. He prepared 47 as many red badges as blue badges. He sold 15 of the red badges and 415 of the blue badges. At the end, 29 more blue badges than red badges remained.
- Show that the ratio of red badges to blue badges prepared was 4 : 7.
- Find the numbers of red badges and blue badges remaining after the sale.
- Find the number of red badges that Ravi sold.
Need a hint?
Red : blue = 4 : 7. Split each part into 15 units so that 15 of the red badges and 415 of the blue badges are whole numbers of units.
Worked answer
- (a) Ravi prepared 47 as many red badges as blue badges, so red : blue = 4 : 7.
- (b) To take 15 of the red and 415 of the blue easily, split each part into 15 units: red = 4 × 15 = 60 units, blue = 7 × 15 = 105 units.
- Red badges left = 45 × 60 units = 48 units.
- Blue badges left = 1115 × 105 units = 77 units.
- Difference = 77 − 48 = 29 units = 29 badges, so 1 unit = 1 badge.
- There were 48 red badges and 77 blue badges left.
- (c) Red badges at first = 60, so red badges sold = 60 − 48 = 12.
Answer: 12 badges
The mistake this question tests
Habit
Fraction of a remainder
A common mistake is to work out 415 − 15 = 115 and say it stands for 29 badges, as if both colours started with the same number. The red and blue badges started in the ratio 4 : 7.
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