Felix and Matthew split a sum of money between them in the ratio [tex]$5:7$[/tex].

If Matthew has £20 more than Felix, what was the total amount that they split?

Give your answer in pounds (£).



Answer :

To determine the total amount Felix and Matthew split based on the given conditions, follow these steps:

1. Define the ratio and the difference:
- Felix and Matthew split the money in a ratio of 5:7.
- Matthew has £20 more than Felix.

2. Set up the relationship between their shares:
- Let Felix’s share be represented as [tex]\(5x\)[/tex] (since the ratio’s first part is 5).
- Let Matthew’s share be represented as [tex]\(7x\)[/tex] (since the ratio’s second part is 7).

3. Express the given information in mathematical form:
- According to the problem, the difference between their shares is £20.
- Therefore, we can write the equation:
[tex]\[ 7x - 5x = 20 \][/tex]

4. Solve the equation for [tex]\(x\)[/tex]:
- Simplify the equation:
[tex]\[ 2x = 20 \][/tex]
- Divide both sides by 2:
[tex]\[ x = 10 \][/tex]

5. Determine each person’s share:
- Felix's share is [tex]\(5x\)[/tex]:
[tex]\[ 5 \times 10 = 50 \][/tex]
Therefore, Felix's share is £50.
- Matthew's share is [tex]\(7x\)[/tex]:
[tex]\[ 7 \times 10 = 70 \][/tex]
Therefore, Matthew's share is £70.

6. Calculate the total amount they split:
- The total amount of money is the sum of Felix's and Matthew's shares:
[tex]\[ 50 + 70 = 120 \][/tex]

Therefore, the total amount that Felix and Matthew split is £120.