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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 coun... 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
Explain why Sharon is not correct.
Answer
Sharon is incorrect because the proportions of red counters in each bag are based on different total counts of counters.
In Bag A, the ratio of red to yellow counters is 1:4. This means for every 1 red counter, there are 4 yellow counters. If we let the number of red counters be ( x ), then the number of yellow counters would be ( 4x ). The total number of counters in Bag A is ( x + 4x = 5x ), and the proportion of red counters is:
In Bag B, ( \frac{1}{4} ) of the total counters are red. If the total number of counters in Bag B is also ( T ), then the number of red counters is ( \frac{1}{4}T ). Therefore, the proportion of red counters in Bag B is:
Thus, the proportions are different: ( \frac{1}{5} ) in Bag A and ( \frac{1}{4} ) in Bag B. This discrepancy means that Sharon's assertion is not correct.
Step 2
Complete the table below to show how many counters of each colour could be in the bags.
Answer
To fill in the table, we will express the counts of red and yellow counters in terms of a common multiple for consistency.
Let us assume that each bag contains ( 20 ) counters (as this is a common multiple that fits both ratios). For Bag A:
- The number of red counters is ( \frac{1}{5} \times 20 = 4 ).
- The number of yellow counters is ( 20 - 4 = 16 ).
For Bag B:
- The number of red counters is ( \frac{1}{4} \times 20 = 5 ).
- The number of yellow counters is ( 20 - 5 = 15 ).
So the completed table would look as follows:
| Red counters | Yellow counters |
|---|---|
| Bag A | 4 |
| Bag B | 5 |
Note: The numbers can vary as long as they respect the given ratios and total count.