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?
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: [tex] x-75=1\frac{1}2\cdot\frac{x-15}{4} [/tex]
[tex] x-75=\frac{3}2\cdot\frac{x-15}{4} [/tex]
Multiply both sides by 8: [tex]8x-8\cdot75=3\cdot(x-15)[/tex]
[tex]8x-600=3x-45[/tex]
Add 600 and subtract 3x on both sides: [tex]5x=555[/tex]
