How many liters of a solution that is 10 percent alcohol by volume must be added to 2 liters of solution that

is 50 percent alcohol by volume to create a solution that is 15 percent alcohol by volume

Distances of concentrations of input from target are:
50 - 15 = 35
15 - 10 = 5
Reverse those to determine the proportions:
5/5 = 1 part of 50% = 2 liters
35/5 = 7 parts of 10% = 14 liters ← Answer

Checking:
14 * .10 = 1.40
2 * .50 = 1.00
Total = 2.40
and 2.40 / 16 = 15% as required

x = number of liters required

(10/100)*x + (50/100)*2 = (15/100)*(x + 2)

(0.1x) + (1) = (3x/20) + (3/10) = (3x/20) + (6/20)

(0.1x) + (1) = (3x/20) + (6/20)

Multiply both sides by 20:

2x + 20 = 3x + 6

2x + 20 - 2x = 3x - 2x + 6

20 = x + 6

x + 6 - 6 = 20 - 6

x = 14 liters