Medium3 marksStructured
AQA GCSE · Question 04 · Number
To the nearest pound, Rosie has £12. She wants to buy 6 drinks. Each drink costs £1.89. Show that Rosie definitely has enough money to buy the 6 drinks.
To the nearest pound, Rosie has £12. She wants to buy 6 drinks. Each drink costs £1.89. Show that Rosie definitely has enough money to buy the 6 drinks.
How to approach this question
1. Understand what "to the nearest pound" means in terms of upper and lower bounds.
2. Find the minimum possible amount of money Rosie could have (the lower bound).
3. Calculate the total cost of the 6 drinks.
4. Compare the minimum amount of money with the total cost to show that the minimum amount is still greater than or equal to the cost.
Full Answer
The phrase "to the nearest pound" implies we need to consider the limits of accuracy, or bounds.
Rosie has £12 to the nearest pound. This means the actual amount of money she has is between £11.50 (inclusive) and £12.50 (exclusive).
To be certain she has enough money, we must check if the minimum possible amount she has is enough to cover the cost.
The lower bound of her money is £11.50.
Next, we calculate the total cost of the drinks:
Cost = 6 drinks × £1.89/drink = £11.34.
Finally, we compare her minimum possible money with the cost:
£11.50 is greater than £11.34.
Since the least amount of money she could possibly have is more than the cost of the drinks, she definitely has enough money.
Common mistakes
✗ Using £12 instead of the lower bound £11.50. This doesn't prove she *definitely* has enough.
✗ Calculating the upper bound (£12.49 or £12.50) which is irrelevant to the question.
✗ Making a calculation error in 6 × £1.89.
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