Find the number of gallons needed of each solution

Question

a chemistry lab needs to make 100 gallons of an 18% acid solution by mixing a 12% acid solution with a 20% acid solution

Answer 1

 

 X + Y = 100 --> Y = 100 - x

 

The amount of acid is 0.12X + 0.2Y = 18

 

 0.12X + 0.2(100 - x) = 18

 

 12X + 20(100 - x) = 1800

 

12x + 2000 - 20x = 1800

 

 -8x = -200

 

 x = -200/-8 = 25

 

25 gallons of 12% acid solution

75 gallon of 20% acid solution

 

CHECK: 25 x 0.12 + 0.2 x 75 = 18 = 0.18 x 100 , so yes it works