felix and mathew split A SUM of money between them in ratio 5:7.if mathew has £20 more than felix what was total amount they split in pounds

Let the total amount of money be \( x \) pounds.

Felix and Mathew split the money in the ratio \( 5:7 \). Therefore, Felix's share is \( \frac{5}{12}x \) and Mathew's share is \( \frac{7}{12}x \).

According to the problem, Mathew has £20 more than Felix. This can be written as:
\[ \frac{7}{12}x = \frac{5}{12}x + 20 \]

To solve for \( x \), we subtract \( \frac{5}{12}x \) from both sides:
\[ \frac{7}{12}x - \frac{5}{12}x = 20 \]
\[ \frac{2}{12}x = 20 \]
\[ \frac{1}{6}x = 20 \]

Now, multiply both sides by 6:
\[ x = 120 \]

Therefore, the total amount of money they split is £120.

Would you like more details or have any questions? Here are some questions you might consider:

1. How do we simplify the fractions in a ratio problem?
2. What if the ratio were different, how would the solution change?
3. Can you explain the steps to solve the equation in more detail?
4. What are some other common types of ratio problems?
5. How do we verify the solution is correct?

**Tip:** Always check your solution by substituting the values back into the original conditions to ensure accuracy.

Discover how to solve ratio problems where one person's amount is more than another's by £20. This example covers the concept of ratios, algebraic equations, and solving for the total amount. Perfect for Grades 7-9.

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