Question

Ryan and Marie had some marbles. if Ryan lost `15 marbles, he would have 4 times as many marbles as Marie. If Ryan lost 75 marbles,, he would have 11/2 times as many marbles as Marie. How many marbles did Ryan have at first?

Answer 1

Ryan's marbles = x
Marie has 4 times less marbles then Ryan would have if he lost 15 marbles (it means he would have x-15)
So, Marie marbles = (x-15):4
If Ryan lost 75 marbles (it means he would have x-75), he would have 1 1/2 times as many marbles as Marie.

We got an equation:
`x-75=1\frac{1}2\cdot(x-15)/(4)`


`x-75=\frac{3}2\cdot(x-15)/(4)`

Multiply both sides by 8:
`8x-8\cdot75=3\cdot(x-15)`


`8x-600=3x-45`

Add 600 and subtract 3x on both sides:
`5x=555`

Divide both sides by 5:
`x=111`


Answer: Ryan have 111 marbles.