- Eli gets £180
- Freda gets £260
- Geoff gets £360
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.