**Answers:**

**Eli gets £180 ****Freda gets £260****Geoff gets £360**

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Explanation:

Let x be some positive real number.

Since each person gets a share of the money based on their ages, we can say that

- Eli gets 9x pounds
- Freda gets 13x pounds
- Geoff gets 18x pounds

The ratio 9x:13x:18x reduces to 9:13:18 when dividing everything by x.

Add up their shares, set the sum equal to 800 pounds, and solve for x.

9x+13x+18x = 800

40x = 800

x = 800/40

x = 20

We can then use this to find each person's share

- Eli = 9x = 9*20 = 180 pounds
- Freda = 13x = 13*20 = 260 pounds
- Geoff = 18x = 18*20 = 360 pounds

As a check: 180+260+360 = 800 which confirms we have the correct split among the three people.

Notice how the ratio 180:260:360 fully reduces to 9:13:18 when you divide each part by the GCF 20.