let

x = gal of the 10% acidic solution

y = gal of the 15% acidic solution

10% acidic solution is combined with a 15% acidic solution to produce 15 gallons of a 12% acidic solution

x + y = 15

0.10x + 0.15y = 0.12*15

by solving the above system of equations we find

x = 9 gal

y = 6 gal

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6 gallons of the 15% acidic solution should be used.