precalculus help

Question

A forester mixes gasoline and oil to make 2 gallons of mixture for a two-cycle chainsaw engine. This mixture is 32 parts gasoline and 1 part oil. How much gasoline must be added to bring the mixture to 48 parts gasoline and 1 part oil?

Answer 1

Let g be the gallons of gasoline added.

The final fraction of gasoline in the mixture is 48/49

The amount of gasoline / total volume after adding x gallons of gas is

((32/33)(2) + x)/(2+x) = 48/49 (multiply out)

64/33 + x = 96/49 + (48/49)x (group and solve)

(1/49)x = 96/49 - 64/33 x = 96 - 49(64)/33 = 32/33

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