A toy shop stocked toy cars and toy robots. Mr Rahman took out 20 toy cars and 80% of the toy robots. When he had finished, the toy cars and toy robots left were in the ratio 3 : 2.
- Write the portion of the toy robots taken out as a fraction in simplest form.
- At first, the shop had 120 more toy robots than toy cars. How many toy cars were there at first?
Need a hint?
For (a), convert the percentage to a fraction. For (b), use a bar model for the ratio of the toys left and work backwards from the fraction of robots that remained.
Worked answer
- (a) 80% = 80100 = 45, so 45 of the toy robots were taken out.
- (b) The toys left were in the ratio 3 : 2: 3 units of toy cars and 2 units of toy robots.
- Only 15 of the toy robots were left, so 2 units = 15 of the toy robots at first.
- Toy robots at first = 2 × 5 = 10 units.
- Toy cars at first = 3 units + 20.
- There were 120 more robots than cars: 10 units − 3 units − 20 = 120.
- 7 units = 140, so 1 unit = 20.
- Toy cars at first = 3 × 20 + 20 = 80.
Answer: 80 toy cars
The mistake this question tests
Habit
Fraction of a remainder
A common wrong path is to apply the 3 : 2 ratio to the original stock. That ratio describes only the toys left after Mr Rahman took some out.
How to fix it at home →Wrong answers children often give:
- 60 Fraction of a remainder
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