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.
