Let's solve the problem step by step.

Step 1: Understand the ratio

Felix and Matthew share the money in the ratio $5 : 7$. This means:

• Felix's share is $5x$
• Matthew's share is $7x$

Here, $x$ is the proportional multiplier.

Step 2: Use the information about the difference

We are told that Matthew has £20 more than Felix. Using the difference:

$7x - 5x = 20$

Simplify:

$2x = 20$

Solve for $x$:

$x = 10$

Step 3: Calculate their shares

Substitute $x = 10$ into $5x$ and $7x$:

• Felix's share = $5x = 5(10) = 50$
• Matthew's share = $7x = 7(10) = 70$

Step 4: Find the total amount split

The total amount is the sum of their shares:

$50 + 70 = 120$

Final Answer:

The total amount they split is £120.

Would you like me to explain any step in more detail or solve related problems? Here are some related questions you might find interesting:

1. What would the shares be if the ratio was $3 : 4$ instead of $5 : 7$?
2. If Felix's share is increased by £10, how does the total amount change?
3. How would the problem change if Matthew had £50 more than Felix instead of £20?
4. If they split the total amount among three people in the ratio $5 : 7 : 8$, what would each person get?
5. How is solving ratio problems useful in budgeting and finance?

Tip: Always double-check your understanding of ratios and the multiplier when solving similar problems.