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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 is the best value for money, we need to calculate the price per milliliter for each size of milk carton.
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300 ml carton for 31p:
Price per ml = ( \frac{31 \text{p}}{300 \text{ml}} = 0.1033 \text{p/ml} )
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500 ml carton for 47p:
Price per ml = ( \frac{47 \text{p}}{500 \text{ml}} = 0.094 \text{p/ml} )
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2 litres (2000 ml) for £1.96:
Price per ml = ( \frac{196 \text{p}}{2000 \text{ml}} = 0.098 \text{p/ml} )
After calculating the price per milliliter:
- The 300 ml carton costs approximately 0.1033 p/ml.
- The 500 ml carton costs 0.094 p/ml.
- The 2 litres carton costs 0.098 p/ml.
Thus, the 500 ml carton offers the best value for money at 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 consumption: 120 ml per day.
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Total milk needed for a week: Given that the student uses milk only on Saturday, we need to calculate the total milk for 7 days:
- Total needed = 120 ml/day * 7 days = 840 ml.
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Number of 300 ml cartons required:
- ( \frac{840 \text{ml}}{300 \text{ml/carton}} = 2.8 ) cartons.
- Since we cannot buy a fraction of a carton, we round up to 3 cartons.
- Total cost for 3 cartons = 3 * 31p = 93p.
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Number of 500 ml cartons required:
- ( \frac{840 \text{ml}}{500 \text{ml/carton}} = 1.68 ) cartons.
- Rounding up gives us 2 cartons.
- Total cost for 2 cartons = 2 * 47p = 94p.
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Comparison of costs:
- Cost of 300 ml cartons: 93p.
- Cost of 500 ml cartons: 94p.
Thus, it is cheaper for the student to buy the milk they need in 300 ml cartons.