Sure, let's solve this problem step by step.
1. Understanding the Ratio: We first look at the ratio of how Andrew, Holly, and Pat share the money, which is [tex]\(2:4:5\)[/tex]. This means for every part of money Andrew gets, Holly gets twice as much, and Pat gets two and a half times as much as Andrew.
2. Identify the Additional Amount: Pat receives £60 more than Andrew. This information helps us relate the parts of the ratio directly to actual amounts.
3. Calculate the Difference in Parts:
- The difference in parts between Pat and Andrew can be calculated from the ratio [tex]\(5 - 2 = 3\)[/tex].
- This tells us that the difference in their portions as per the ratio is 3 parts.
4. Value of One Part: Given that this difference (3 parts) is equivalent to £60, we can calculate the value of each part by dividing £60 by 3:
[tex]\[
\text{Value of one part} = \frac{60}{3} = 20
\][/tex]
5. Calculate Individual Shares:
- Andrew's share = 2 parts
[tex]\[
\text{Andrew's amount} = 2 \times 20 = 40
\][/tex]
- Holly's share = 4 parts
[tex]\[
\text{Holly's amount} = 4 \times 20 = 80
\][/tex]
- Pat's share = 5 parts
[tex]\[
\text{Pat's amount} = 5 \times 20 = 100
\][/tex]
Thus, the amount of money each person gets is:
- Andrew: £40
- Holly: £80
- Pat: £100
