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There are $p$ counters in a bag - Edexcel - GCSE Maths - Question 12 - 2019 - Paper 1

Question 12

There are $p$ counters in a bag. 12 of the counters are yellow. Shafiq takes at random 30 counters from the bag. 5 of these 30 counters are yellow. Work out an est... show full transcript

Worked Solution & Example Answer:There are $p$ counters in a bag - Edexcel - GCSE Maths - Question 12 - 2019 - Paper 1

Step 1

Using Proportions

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Answer

The number of yellow counters Shafiq took is 5 out of the 30 counters he picked.

To set up a proportion based on the total number of yellow counters, we have: $\frac{12}{p} = \frac{5}{30}$

This means that the fraction of yellow counters in the bag should equal the fraction of yellow counters in the sample.

Step 2

Solving the Proportion

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Answer

Cross-multiplying gives us: $12 \times 30 = 5 \times p$ This simplifies to: $360 = 5p$

Now, divide both sides by 5 to solve for $p$ : $p = \frac{360}{5} = 72$ .

Step 3

Conclusion

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Answer

Thus, the estimated value of $p$ is 72.

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