Question

The ratio of the number of Miki's stickers to the number of Ken's

stickers was 8:7. After Miki gave Ken 18 of her stickers, they had
the same number of stickers. How many stickers did they have in all?

Answer 1

Miki had 288 stickers and Ken had 252 stickers.

Explanation:

This question is solved using a system of equations.

I am going to say that:

Miki has x stickers.

Ken has y stickers.

The ratio of the number of Miki's stickers to the number of Ken's stickers was 8:7.

This means that
`(x)/(y) = (8)/(7)`, that is:
`7x = 8y`, or
`x = (8y)/(7)`

After Miki gave Ken 18 of her stickers, they had the same number of stickers.

This means that:

`x - 18 = y + 18`

`x - y = 36`

Since
`x = (8y)/(7)`

`(8y)/(7) - y = 36`

`(8y)/(7) - (7y)/(7) = 36`

`(y)/(7) = 36`

`y = 36*7 = 252`

And

`x - y = 36`

`x = 36 + y = 36 + 252 = 288`

Miki had 288 stickers and Ken had 252 stickers.