Question

Leonie bought a hat and coat.

The hat cost £6.

She sold both items for a total of £45

Leonie made a 300% profit on the hat and a 125% profit on the total cost.

Work out her percentage profit on the cost of the coat

Answer 1

Leonie made a 78.85% profit on the cost of the coat.

Step-by-step explanation:

To calculate Leonie's percentage profit on the cost of the coat, we need to find the cost of the coat and the profit she made on it. We know that she made a 300% profit on the hat and a 125% profit on the total cost of both items combined. Let's solve it step by step:

1. Let's find the total cost of both items.
   The hat cost £6, so the cost of the coat will be the total amount - £6.
   Total cost = £45 - £6 = £39
2. Let's find the profit Leonie made on the total cost.
   She made a 125% profit on the total cost, so the profit will be 125% of £39.
   Profit = 125% of £39 = 1.25 * £39 = £48.75
3. Now, let's find the profit Leonie made on the coat.
   The profit on the coat will be the total profit - profit on the hat.
   Profit on the coat = £48.75 - (£6 * 3) = £48.75 - £18 = £30.75
4. Finally, let's find the percentage profit on the cost of the coat.
   Profit percentage = (Profit on the coat / Cost of the coat) * 100%
   Profit percentage = (£30.75 / £39) * 100% = 78.85% (rounded to the nearest decimal)

Answer 2

Leonie's percentage profit on the cost of the coat is 50%, which is calculated by determining the original combined cost based on the total profit margin, subtracting the known cost of the hat, and then finding the profit on the coat.

Step-by-step explanation:

Leonie made a 300% profit on the hat, which cost £6, so the sale price of the hat was £24 (since 300% of £6 is £18 and adding that to the original cost gives £24). If she sold both the hat and coat for a total of £45 and the hat was £24 of that, then the coat sold for £45 - £24 = £21. Given that she made a 125% profit on the total cost, we can find the total original cost of both items. A 125% profit means the sale price is 225% of the original cost (100% + 125%). Thus, the calculation is £45 = 225% of the original cost, so the original cost is £45 / 2.25 = £20. The original cost of the coat will be the original total cost minus the cost of the hat: £20 - £6 = £14. To find the profit on the coat, subtract the original cost of the coat (£14) from the sale price of the coat (£21) to get a profit of £7. Therefore, the percentage profit on the cost of the coat is (profit/cost) * 100% = (£7/£14) * 100% = 50%.

The answer is that Leonie's percentage profit on the cost of the coat is 50%.