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

The probability of picking a blue counter from the bag is given as ( \frac{23}{50} ). To find the number of blue counters, we can use the equation:

$\text{Number of blue counters} = \text{Total counters} \times \text{Probability of blue counter}$

Substituting the values:

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

Step 2

Determine the number of white counters

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Answer

Let ( r ) be the number of red counters and ( w ) be the number of white counters. According to the ratio of red to white counters which is 2:1, [ r = 2w ]

Since the total number of counters is 300, we write the equation: [ r + w + 138 = 300 ] Substituting ( r = 2w ) into the equation: [ 2w + w + 138 = 300 ] [ 3w + 138 = 300 ] [ 3w = 162 ] [ w = 54 ]

Thus, the number of white counters is 54.

Step 3

Calculate the number of red counters

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Answer

Using the value of white counters to find red counters: [ r = 2w = 2 \times 54 = 108 ]

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

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