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A shop sells the same milk in three different sized cartons - OCR - GCSE Maths - Question 6 - 2021 - Paper 1
Question 6
A shop sells the same milk in three different sized cartons. The diagram shows the price of each carton. Which carton is the best value for money? Show how you deci... show full transcript
Worked Solution & Example Answer:A shop sells the same milk in three different sized cartons - OCR - GCSE Maths - Question 6 - 2021 - Paper 1
Step 1
Which carton is the best value for money?
Answer
To determine which carton offers the best value for money, we will calculate the price per milliliter for each carton:
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300 ml carton:
It costs 31p, so: [ ext{Cost per ml} = \frac{31}{300} \approx 0.1033 ext{ p/ml} ]
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500 ml carton: It costs 47p, so: [ ext{Cost per ml} = \frac{47}{500} = 0.094 ext{ p/ml} ]
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2 litres (2000 ml) carton: It costs £1.96 (or 196p), so: [ ext{Cost per ml} = \frac{196}{2000} = 0.098 ext{ p/ml} ]
Conclusion: The 500 ml carton provides the best value for money at approximately 0.094 p/ml.
Step 2
Show that it is cheaper for the student to buy the milk they need in 300 ml cartons than in 500 ml cartons.
Answer
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Daily milk usage: The student uses 120 ml of milk each day.
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Total milk needed for one week:
In total, they need: [ 120 ext{ ml/day} \times 7 ext{ days} = 840 ext{ ml} ]
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Cost for 300 ml cartons:
The number of cartons required would be: [ \frac{840 ext{ ml}}{300 ext{ ml/carton}} \approx 2.8 \quad \text{(round up to 3 cartons)} ] The total cost would be: [ 3 \times 31 ext{ p} = 93 ext{ p} ]
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Cost for 500 ml cartons:
The number of cartons required would be: [ \frac{840 ext{ ml}}{500 ext{ ml/carton}} = 1.68 \quad \text{(round up to 2 cartons)} ] The total cost would be: [ 2 \times 47 ext{ p} = 94 ext{ p} ]
Conclusion: The cost for 300 ml cartons is 93p, while the cost for 500 ml cartons is 94p. Therefore, it is cheaper for the student to buy 300 ml cartons.