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Two bags each contain only red counters and yellow counters - OCR - GCSE Maths - Question 6 - 2017 - Paper 1
Question 6
Two bags each contain only red counters and yellow counters. In Bag A, the ratio of red counters to yellow counters is 1 : 4. In Bag B, \( \frac{1}{4} \) of the c... show full transcript
Worked Solution & Example Answer:Two bags each contain only red counters and yellow counters - OCR - GCSE Maths - Question 6 - 2017 - Paper 1
Step 1
(i) Explain why Sharon is not correct.
Answer
Sharon is not correct because the proportions of red counters to total counters differ between the two bags. In Bag A, the ratio of red to yellow counters is 1:4, meaning there are 1 red counter for every 4 yellow counters. This gives a proportion of red counters as follows:
In Bag B, where ( \frac{1}{4} ) of the counters are red, the proportion of red counters is:
Thus, the proportions of red counters are not the same: 20% in Bag A and 25% in Bag B.
Step 2
(ii) Complete the table below to show how many counters of each colour could be in the bags.
Answer
Assuming the total number of counters in both bags is the same, the quantities can be calculated. Let the total number of counters in each bag be ( n ).
In Bag A:
- Red Counters = ( x = 1 \cdot k )
- Yellow Counters = ( y = 4 \cdot k )
Total in Bag A: ( n = x + y = k + 4k = 5k )
In Bag B:
- Since ( \frac{1}{4} ) are red, we have ( \text{Red} = \frac{n}{4} )
- The remaining counters will be yellow, thus ( \text{Yellow} = n - \frac{n}{4} = \frac{3n}{4} )
This implies:
- For Bag A, if we let k = 1, then:
- Red = 1, Yellow = 4, Total = 5
- For Bag B to keep the same total:
- Red = 1, Yellow = 3 (as an example keeping total as a multiple of 4)
Hence, the filled table could look like:
| Bag A | 1 | 4 | | Bag B | 1 | 3 |