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A £1 coin weighs 8.75g; correct to the nearest 0.01g - OCR - GCSE Maths - Question 16 - 2018 - Paper 6
Question 16
A £1 coin weighs 8.75g; correct to the nearest 0.01g. Mitul weighs the contents of a large bag of £1 coins. The coins weigh 2.63kg, correct to the nearest 10g. Mitu... show full transcript
Worked Solution & Example Answer:A £1 coin weighs 8.75g; correct to the nearest 0.01g - OCR - GCSE Maths - Question 16 - 2018 - Paper 6
Step 1
Calculate the bounds for the number of coins
Answer
The weight of the coins is 2.63kg, which is equivalent to 2630g. Since this measurement is correct to the nearest 10g, the possible range of weights is:
- Lower bound: 2630g - 5g = 2625g
- Upper bound: 2630g + 5g = 2635g
Thus, the number of coins is calculated as follows:
- Lower bound: ( \frac{2625g}{8.75g} \approx 300 \text{ coins} )
- Upper bound: ( \frac{2635g}{8.75g} \approx 301.43 \text{ coins} ), rounding down gives 301 coins.
Step 2
Mitul's Calculation
Answer
Mitul states that he believes the coins add up to £300 based on: ( 2625 + 8.755 = 299.8 ) This suggests he is using the weight of a single coin at its upper bound (8.755g). However, we must consider the lower bound of the weight for the total number of coins, which could potentially lead to a sum under £300.
Thus,
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Considering the lower bound for the count of coins (300) at the lower limit: ( 300 \text{ coins} \times 8.75g = 2625g ) This confirms he is using the correct lower boundary, but using the upper bound for the weight leads to an estimation that might suggest there are enough coins, when in fact:
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The total money calculated is: ( 300 \text{ coins} \times £1 = £300 ) This does not account for possible deviations in weight that could suggest fewer coins.
Step 3