Question

How much pure antifreeze should be added to 3 gallons of a 30 percent antifreeze solution to get 65 percent antifreeze?

Answer 1

The easiest way to solve mixture problems is to do a CMB ( Component Material Balance). We also take note that when it is pure it means 100%.

we let x be the number of gallons of anti freeze, to be added

to the 3 gallons ( 30% antifreeze solution), so therefore the total volume after mixing is X+3 which is ( 65% antifreeze)

we do an anti freeze balance,,

100%(X) + 30%( 3) = 65% ( x+3)

then we solve for x, 100% is 1, 30% is 0.3, 65% IS 0.65

X + 0.9 = 0.65( X + 3)

X + 0.9 = 0.65X + 1.95

X - 0.65X = 1.95 - 0.9

0.35X = 1.05

divide by 0.35 both sides

X= 3 gallons of pure antifreeze