help with ratio

 How much money did Mario have at first?

Hello Guest!

\(m:l=9:4\\ l=\dfrac{4m}{9}\\ (m-\$84):l=1:2\\ l=2m-\$168\)

\(\dfrac{4m}{9}=2m-\$168\\ 4m=18m-\$1512\\ 14m=\$1512\)

\(m=\$108\)

\(Mario\ initially\ had\ \ \color{blue}$ 108.\)

  !

It was answered  in https://web2.0calc.com/questions/ratio_42

M --> Mario's

L--> Luigi's

According to question:

\( {M \over 4} = {9 \over 4}\)

4M = 9L ---- eq¹(1)

Again \( {M - 84 \over L } = {1 \over 2}\)
           2M - 168 = L ---- equation (2)

     Putting the value of in equation (1)

           4M = 9(2M - 168)

           4M = 18M - 1512

           14M = 1512

              M = \({1512\over14 } = 108\)
              M = 108

         the ratio have at first money is $108