Mixture Problems and Systems of Linear Equations in Two Variables

Question

A scientist needs 60 liters of a 40% solution of alcohol. He has a 30% solution and a 60% solution available. How many liters of the 30% solution and how many liters of the 60% solution should he mix to make the 40% solution?

Answer 1

For 60 liters of 40% solution, write x = number of liters of 30% solution and y = number of liters of 60% solution.

Then equate 0.30x + 0.60y to 0.40(60) and write:

0.30x + 0.60y = 24

x + y = 60

Multiply (x + y = 60) by 0.30 to obtain 0.30x + 0.30y = 18.

0.30x + 0.60y = 24 (Equation A)

0.30x + 0.30y = 18 (Equation B)

0.30y = 6 (Equation A - Equation B)

Subtracting Equation B from Equation A gives 0.30y = 6 or y = 20 liters of 60% solution.

Putting y = 20 into (Equation A) gives 0.30x + 0.60(20) = 24 or x = 40 liters of 30% solution.