Question

The ratio of money in Obi's wallet to Rudy's wallet one day was 5:2.

Obi spent £20 that day.
Obi now had £8 less than Rudy.
How much did Obi initially have?

Answer 1

The amount that Obi initially had was £20

Explanation:

Let

x ----> amount that Obi initially has

y ----> amount that Rudy has

we know that

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

`x=2.5y` ----> equation A

`x-20=y-8`

`y=x-20+8`

`y=x-12` ----> equation B

Solve the system by substitution

substitute equation A in equation B

`y=(2.5y)-12`

solve for y

`2.5y-y=12\\1.5y=12\\y=8`

Find the value of x

`x=2.5(8)=20`

therefore

The amount that Obi initially had was £20