Question

Leo, Kush and Mai share some money in the ratio 3:5:8

Kush receives £750 more than Leo.
Calculate total amount of money that they shared.

Answer 1

The total amount of money that they shared is
`\£6,000`

Explanation:

Let

x-----> amount of money Leo shares

y-----> amount of money Kush shares

z-----> amount of money Mai shares

we know that

`(x)/(y) =(3)/(5)`

`x=(3)/(5)y` -----> equation A

`(y)/(z) =(5)/(8)`

`z=(8)/(5)y` -----> equation B

`(x)/(z) =(3)/(8)`

`z=(8)/(3)x` -----> equation C

`y=x+750` ------> equation D

substitute equation A in equation D and solve for y

`y=(3)/(5)y+750`

`y-(3)/(5)y=750`

`(2)/(5)y=750`

`y=750*5/2=\£1,875`

Find the value of x (equation A)

`x=(3)/(5)(1,875)=\£1,125`

Find the value of z (equation C)

`z=(8)/(3)(1,125)=\£3,000`

therefore

The total amount of money is equal to

`x+y+z=\£1,125+\£1,875+\£3,000=\£6,000`