Kim is a driving instructor. Kim charges £30 for a one-hour lesson. Her fixed costs are £14,000 per annum. The variable cost for a one-hour lesson is £6. How many one-hour lessons will Kim need to give before making a profit? A 389 lessons B 467 lessons C 584 lessons D 2334 lessons Your answer ____

GCSE OCR Business Revenue, costs and profits: Kim is a driving instructor. Kim

Kim is a driving instructor - OCR - GCSE Business - Question 6 - 2021 - Paper 1

Question 6

Kim is a driving instructor. Kim charges £30 for a one-hour lesson. Her fixed costs are £14,000 per annum. The variable cost for a one-hour lesson is £6. How many o... show full transcript

Worked Solution & Example Answer:Kim is a driving instructor - OCR - GCSE Business - Question 6 - 2021 - Paper 1

Step 1

Calculate Total Costs

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Answer

To find out how many lessons Kim needs to give to make a profit, first, we need to calculate the total costs, which include fixed and variable costs.

The fixed costs are £14,000 per annum, and the variable cost per lesson is £6. If Kim gives x lessons, then the total variable costs will be 6x.

Thus, the total cost can be expressed as:

[ Total \ Cost = Fixed \ Cost + Variable \ Cost = 14000 + 6x ]

Step 2

Calculate Revenue from Lessons

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Answer

Next, we calculate the total revenue from the lessons. Kim charges £30 per one-hour lesson, so if she teaches x lessons, her total revenue will be:

[ Total \ Revenue = 30x ]

Step 3

Set Up the Equation for Profit

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To make a profit, the total revenue must be greater than the total costs. Therefore, we set up the following inequality:

[ 30x > 14000 + 6x ]

Step 4

Solve the Inequality

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Now, we solve this inequality step by step:

Subtract 6x from both sides: [ 30x - 6x > 14000 ] [ 24x > 14000 ]
Divide both sides by 24: [ x > \frac{14000}{24} \approx 583.33 ]

Since x must be a whole number, Kim needs to give at least 584 lessons to start making a profit.

Step 5

Final Answer

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Answer

Thus, the minimum number of one-hour lessons Kim needs to give before making a profit is 584 lessons. Therefore, the correct option is C.

Kim is a driving instructor - OCR - GCSE Business - Question 6 - 2021 - Paper 1

Worked Solution & Example Answer:Kim is a driving instructor - OCR - GCSE Business - Question 6 - 2021 - Paper 1

Calculate Total Costs

Calculate Revenue from Lessons

Set Up the Equation for Profit

Solve the Inequality

Final Answer

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