Adam, Tara and Sophia share a sum of money in the ratio 2:5:14Adam got £40.How much did Sophia receive

1. Break Down the Problem

We are given the ratio of the shares of Adam, Tara, and Sophia as 2:5:14. We need to find out how much Sophia received given that Adam received £40.

2. Relevant Concepts

Let:

• Adam's share = 2x
• Tara's share = 5x
• Sophia's share = 14x

From the problem, we know that Adam received £40, which corresponds to 2x.

3. Analysis and Detail

1. Set up the equation based on Adam's share: $2x = 40$
2. Solve for $x$: $x = \frac{40}{2} = 20$
3. Now calculate Sophia's share: $\text{Sophia's share} = 14x = 14 \times 20 = 280$

4. Verify and Summarize

To ensure everything is correct, we can check the total ratio:

• Adam: $2x = 40$
• Tara: $5x = 5 \times 20 = 100$
• Sophia: $14x = 280$

Total will be: $40 + 100 + 280 = 420$ The ratios are $2:5:14$ with total parts $2 + 5 + 14 = 21$. Each part represents:

• Adam: $\frac{2}{21} \times 420 = 40$
• Tara: $\frac{5}{21} \times 420 = 100$
• Sophia: $\frac{14}{21} \times 420 = 280$

Final Answer

Sophia received £280.