Lily buys and sells microwaves. She buys each one for £32 and sells it for £60. She also pays £7 for the delivery of each microwave she sells. If she sells a microwave that is faulty then Lily must pay for its repair and redelivery. This costs her another £25 for each faulty microwave. Last month, 6 out of the 80 microwaves Lily sold were faulty. This month she has orders for 133 microwaves. Calculate her expected percentage profit on this month’s order. Showing your working in the boxes below may help you present your work.

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Lily buys and sells microwaves - OCR - GCSE Maths - Question 8 - 2020 - Paper 1

Question 8

Lily buys and sells microwaves. She buys each one for £32 and sells it for £60. She also pays £7 for the delivery of each microwave she sells. If she sells a micro... show full transcript

Worked Solution & Example Answer:Lily buys and sells microwaves - OCR - GCSE Maths - Question 8 - 2020 - Paper 1

Step 1

Expected number of faulty microwaves:

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Answer

To find the expected number of faulty microwaves, we first need to determine the ratio of faulty microwaves from last month's sales. From last month, Lily sold 80 microwaves, and 6 were faulty, which gives us the ratio:

$ext{Faulty ratio} = \frac{6}{80} = 0.075$

Now, applying this ratio to this month's order of 133 microwaves:

$ext{Expected faulty microwaves} = 0.075 \times 133 = 9.975 \approx 10$ .

Therefore, the expected number of faulty microwaves is approximately 10.

Step 2

Expected costs:

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Answer

To calculate the expected costs, we need to consider the purchase price, delivery costs, and the costs associated with faulty microwaves.

The cost of each microwave:

Purchase: £32
Delivery: £7 So, total cost per microwave:

$ext{Total cost per microwave} = £32 + £7 = £39$

For 133 microwaves, the total cost becomes:

$ext{Total cost for 133 microwaves} = 133 \times £39 = £5,197$

Next, we calculate the additional costs for the expected 10 faulty microwaves:

Repair and redelivery per faulty microwave: £25 Therefore, total costs for repairs:

$ext{Repairs for 10 faulty} = 10 \times £25 = £250$

Adding this to the total costs:

$ext{Expected Total Costs} = £5,197 + £250 = £5,447$

Step 3

Income from sales:

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Answer

The selling price for each microwave is £60. For 133 microwaves, the total income from sales is:

$ext{Total Income} = 133 \times £60 = £7,980$

Step 4

Expected percentage profit:

98%

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Answer

To find the expected percentage profit, we first calculate the profit:

$ext{Profit} = ext{Income} - ext{Costs} = £7,980 - £5,447 = £2,533$

Next, we calculate the percentage profit using the formula:

$ext{Percentage Profit} = \left( \frac{\text{Profit}}{\text{Costs}} \right) \times 100$

Plugging in the values:

$ext{Percentage Profit} = \left( \frac{£2,533}{£5,447} \right) \times 100 \approx 46.49\%$

Therefore, the expected percentage profit is approximately 46.5%.

Lily buys and sells microwaves - OCR - GCSE Maths - Question 8 - 2020 - Paper 1

Worked Solution & Example Answer:Lily buys and sells microwaves - OCR - GCSE Maths - Question 8 - 2020 - Paper 1

Expected number of faulty microwaves:

Expected costs:

Income from sales:

Expected percentage profit:

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