A £1 coin weighs 8.75g; correct to the nearest 0.01g - OCR - GCSE Maths - Question 16 - 2018 - Paper 6

To assess whether Mitul's claim of the bag containing exactly £300 is correct, we need to examine the bounds of both the weight of the coins and the weight of a single coin.

1. Determine the upper and lower bounds of the weight of the coins:

   • The weight of the coins is given as 2.63 kg, which is correct to the nearest 10g.
   • Thus, the lower bound is: $2630g - 5g = 2625g$
   • The upper bound is: $2630g + 5g = 2635g$

2. Determine the upper and lower bounds of the weight of one £1 coin:

   • The weight of a single £1 coin is 8.75g, correct to the nearest 0.01g.
   • The lower bound is: $8.75g - 0.005g = 8.745g$
   • The upper bound is: $8.75g + 0.005g = 8.755g$

3. Calculate the minimum and maximum possible value of the coins:

   • For the lower bound of the total weight (2625g):
     • Maximum number of coins: rac{2625g}{8.755g} ≈ 299.73
     • Value: $299 * £1 = £299$
   • For the upper bound of the total weight (2635g):
     • Minimum number of coins: rac{2635g}{8.745g} ≈ 301.54
     • Value: $301 * £1 = £301$

4. Conclusion:

   • The actual amount that could be in the bag is between £299 and £301. Therefore, Mitul's statement that the bag contains exactly £300 is uncertain, as it could potentially be £299 or even £301, depending on the exact weight of the coins.