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:                                  $x-75=1\frac{1}2\cdot\frac{x-15}{4}$

                                                                  $x-75=\frac{3}2\cdot\frac{x-15}{4}$

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.