How many gallons of a 30% salt solution must be added to 40 gallons of a 12% salt solution to obtain a 20% solution?

volume = 32 gallons

Explanation:
We will assume that the volumes are additive.
Therefore, the equation that we will use to solve this problem is:
M1V1 + M2V2 = M3V3
where:
M1 is the concentration of the first solution = 30% = 0.3
V1 is the volume of the first solution that we want to calculate
M2 is the concentration of the second solution = 12% = 0.12
V2 is the volume of the second solution = 40 gallons
M3 is the concentration of the resultant solution = 20% = 0.2
V3 is the volume of the resultant solution = (V1+V2) = (V1+40)

Substitute with the givens in the above equation to get V1 as follows:
M1V1 + M2V2 = M3V3
(0.3)V1 + (0.12)(40) = (0.2)(V1+40)
0.3V1 + 4.8 = 0.2V1 + 8
0.3V1 - 0.2V1 = 8 - 4.8
0.1V1 = 3.2
V1 = 32 gallons

Hope this helps :)

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