Ratios

The ratio of Alan's apples to Don's apples was 3:5. When Alan gave 30 of his apples to Don, the ratio of Alan's apples to Don's apples became 1:5. Find the number of apples Alan had at first?     

A / D  =  3 / 5                      crossmultiply ——>>  5A  =  3D     

(A–30) / (D+30)  =  1 / 5     crossmultiply ——>>  5 • (A–30)  =  1 • (D+30)     

5A – 150  =  D + 30     

from (eq 1) 5A = 3D    substitute this into the previous      

3D – 150  =  D + 30     

          2D  =  180     

            D  =  90     

          5A  =  3D     

          5A  =  3 • 90     

          5A  =  270     

            A  =  54     

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