Let’s break down and solve the problem step by step.

Problem Details:

• £600 is shared between Abby, Ben, Chloe, and Denesh.
• The ratio of the amount Abby gets to the amount Ben gets is 2:7.
• Both Chloe and Denesh each receive 1.5 times the amount Abby gets.

Step 1: Define the amounts.

Let:

• Abby's share = $2x$,
• Ben's share = $7x$.

Since Chloe and Denesh each get $1.5 \times \text{Abby’s share}$, their shares are:

• Chloe's share = $1.5 \times 2x = 3x$,
• Denesh's share = $3x$.

Step 2: Total the shares.

The total amount of money shared is £600. Adding the shares gives: $2x + 7x + 3x + 3x = 15x.$

Step 3: Solve for $x$.

The total amount is £600, so: $15x = 600.$ Solve for $x$: $x = \frac{600}{15} = 40.$

Step 4: Calculate each person's share.

• Abby's share = $2x = 2 \times 40 = 80$,
• Ben's share = $7x = 7 \times 40 = 280$,
• Chloe's share = $3x = 3 \times 40 = 120$,
• Denesh's share = $3x = 3 \times 40 = 120$.

Step 5: Verify the total.

Adding the shares: $80 + 280 + 120 + 120 = 600.$ The total matches the given amount, so our calculations are correct.

Final Answer:

The amount of money that Ben gets is £280.

Would you like me to explain any specific step in more detail?

Here are 5 related questions to deepen your understanding:

1. What is the mathematical concept of a ratio, and how is it applied in this problem?
2. How would the solution change if Chloe and Denesh received 2 times Abby’s share instead of 1.5 times?
3. How can you distribute an amount using different ratios between more people (e.g., five people)?
4. If the total amount were changed to £1,200, how would the shares adjust proportionally?
5. What happens if one person's share (e.g., Abby's) is unknown, and only partial ratios are provided?

Tip:

When solving ratio problems, always start by defining variables for the amounts and relate them to the total amount step by step. This ensures clarity and avoids confusion.