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:                                 

                                                                 

Multiply both sides by 8:                           

                                                                 

Add 600 and subtract 3x on both sides:   

Divide both sides by 5:                              

    Ryan have 111 marbles.

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