how many liters of a 10% alcohol solution must be mixed with 20l of a 80% solution to get a 50% solution?

Question

working on linear word equations

Answer 1

how many liters of a 10% alcohol solution must be mixed with 20l of a 80% solution to get a 50% solution?

0.1 * xL + 0.8 * 20L = 0.5 * (20 + x)L
0.1xL + 16L = 10L + 0.5xL
6L = 0.4xL
6L/0.4 = xL
xL = 15L

15L of 10% solution added to 20L of 80% solution gives 35L of 50% solution

.1(15) + .8(20) = .5(35)
1.5 + 16 = 17.5