Question

An experiment calls for 5% salt solution. Only a 3% salt solution and 8% salt solution are available. How many gallons of each must be combined to obtain 30 gallons of 5% salt solution?

Answer 1

18 gallons of the 3% solution

12 gallons of the 8% solution

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Work Shown:

x = amount, in gallons, of 3% solution

30-x = amount of 8% solution

0.03x = amount of pure salt from the 3% solution

0.08(30-x) = amount of pure salt from the 8% solution

0.03x+0.08(30-x) = total amount of pure salt

0.03x+0.08(30-x) = 0.05*30

0.03x+2.4-0.08x = 1.5

-0.05x+2.4 = 1.5

-0.05x= 1.5-2.4

-0.05x= -0.9

x= -0.9/(-0.05)

x= 18 gallons = amount of the 3% solution

30-x = 30-18 = 12 gallons = amount of the 8% solution