A bag contains some counters. - There are 300 counters in the bag. - There are only red, white and blue counters in the bag. - The probability of picking a blue counter is $\frac{23}{50}$. - The ratio of red counters to white counters is 2 : 1. Calculate the number of red counters in the bag.

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A bag contains some counters - OCR - GCSE Maths - Question 6 - 2019 - Paper 6

Question 6

A bag contains some counters. - There are 300 counters in the bag. - There are only red, white and blue counters in the bag. - The probability of picking a blue cou... show full transcript

Worked Solution & Example Answer:A bag contains some counters - OCR - GCSE Maths - Question 6 - 2019 - Paper 6

Step 1

Calculate the number of blue counters

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Answer

Given that the probability of picking a blue counter is $\frac{23}{50}$ , we can find the number of blue counters by multiplying this probability by the total number of counters:

$\text{Number of blue counters} = \frac{23}{50} \times 300 = 138.$

Thus, the number of blue counters is 138.

Step 2

Calculate the number of red and white counters

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Answer

Let the number of white counters be $w$ and the number of red counters be $r$ . The total number of counters can be expressed as:

$r + w + 138 = 300.$

This simplifies to:

$r + w = 162.$

Since the ratio of red counters to white counters is given as 2:1, we can express this as:

$r = 2w.$

Substituting into the previous equation gives:

$2w + w = 162,$

which simplifies to:

$3w = 162 \Rightarrow w = 54.$

Now substituting back to find the number of red counters:

$r = 2 \times 54 = 108.$

Step 3

Conclusion

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Answer

Therefore, the number of red counters in the bag is 108.

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