Question 1065127

We need to add X gallons of 70% drink.

So the amount of juice in the final mixture (14+X)(0.5) must match the amount of juice we started with (0.3*14), plus the amount of 70% to be added (0.7*X):

Therefore  (14+X)(0.5) = (0.3)(14) + (0.7)X
                  14+X = (0.3)(28) + (1.4)X     (multiplied by 2)
                  14+X = 8.4 + 1.4X
                      5.6 = 0.4X
                         X = 5.6/0.4 = 14
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Ans:  Adding {{{highlight(14)}}} gal of 70% drink will bring the original 14 gal 30% drink up to 50%
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Check:  (14+14)(0.5) = 14  and
           (14)(0.3) + (14)(0.7) = 4.2 + 9.8 = 14   (ok)