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The problem provides the following information:

- Alex makes 80 cakes in total, divided into chocolate, lemon, and fruit cakes in the ratio of \( 3 : 2 : 5 \).
- He sells:
  - All of the chocolate cakes,
  - \( \frac{3}{4} \) of the lemon cakes,
  - \( \frac{7}{8} \) of the fruit cakes.

The profit per cake sold is given in a table:
- Chocolate: £2.00
- Lemon: £1.70
- Fruit: £2.40

### Step 1: Determine how many cakes of each type are made.

Since the ratio of chocolate, lemon, and fruit cakes is \( 3:2:5 \), we can divide the 80 cakes into parts. The total number of parts is \( 3 + 2 + 5 = 10 \) parts.

- Number of chocolate cakes = \( \frac{3}{10} \times 80 = 24 \) cakes.
- Number of lemon cakes = \( \frac{2}{10} \times 80 = 16 \) cakes.
- Number of fruit cakes = \( \frac{5}{10} \times 80 = 40 \) cakes.

### Step 2: Calculate how many cakes Alex sells.

- Chocolate cakes: He sells all 24 chocolate cakes.
- Lemon cakes: He sells \( \frac{3}{4} \times 16 = 12 \) lemon cakes.
- Fruit cakes: He sells \( \frac{7}{8} \times 40 = 35 \) fruit cakes.

### Step 3: Calculate the total profit for each type of cake.

- Profit from chocolate cakes = \( 24 \times 2.00 = 48 \) pounds.
- Profit from lemon cakes = \( 12 \times 1.70 = 20.40 \) pounds.
- Profit from fruit cakes = \( 35 \times 2.40 = 84 \) pounds.

### Step 4: Calculate the total profit.

Total profit = \( 48 + 20.40 + 84 = 152.40 \) pounds.

Thus, the total profit that Alex makes from selling the cakes is **£152.40**.

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Do you want further details or have any questions?

Here are 5 related questions:
1. What would the profit be if Alex sold half of the lemon cakes instead of \( \frac{3}{4} \)?
2. How many cakes would Alex have sold in total?
3. How would the profit change if the profit per fruit cake increased to £3.00?
4. If Alex made 100 cakes instead of 80, how would that affect the total profit?
5. What would happen to the profit if Alex sold \( \frac{5}{8} \) of the fruit cakes?

**Tip**: Always start by breaking down ratios into manageable parts when calculating quantities from totals!

Alex makes 80 cakes to sell, with the ratio of chocolate cakes, lemon cakes, and fruit cakes being 3:2:5. He sells all the chocolate cakes, 3/4 of the lemon cakes, and 7/8 of the fruit cakes. The profit per cake is: chocolate £2.00, lemon £1.70, fruit £2.40. Work out the total profit Alex makes from the cakes he sells.

Learn how to calculate the total profit Alex makes from selling cakes. This problem involves ratios, fractions, and multiplication, where Alex sells all his chocolate cakes, 3/4 of his lemon cakes, and 7/8 of his fruit cakes. Suitable for students in Grades 8-10.

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