Question

2) How much 64% acid solution should be mixed with 12 gallons of a 38% acid solution in order to make a 52% acid solution?​

Answer 1

Answer: 14 gallons of the 64% acid solution is needed

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Work Shown:

x = amount, in gallons, of the 64% acid solution

0.64x = amount of pure acid from the stuff we're adding in

0.38*12 = 4.56 = amount of pure acid from 38% solution

In total, we have 0.64x+4.56 gallons of pure acid out of x+12 gallons total

Dividing the two amounts will give us the decimal form of the percentage. Set this equal to 0.52 and solve for x

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(0.64x+4.56)/(x+12) = 0.52

0.64x+4.56 = 0.52(x+12)

0.64x+4.56 = 0.52x+6.24

0.64x-0.52x = 6.24-4.56

0.12x = 1.68

x = 1.68/0.12

x = 14 gallons is the amount of the 64% acid solution we need to add in