How do I find the two equations I need to solve the problem?

Question

You need 4 liters of a 15% saline solution. Mixture X is a 20% saline solution. Mixture Y is a 10% saline solution. How many liters of Mixture X and how many liters of Mixture Y do you need to make a new 15% solution?

Answer 1

Let x = liters of the 20% solution and (4-x) = liters of the 10% solution

Then

{ 20x + 10(4-x) }/4 = 15

So,

20x -10x + 40 = 60

10x = 20

x = 2 liters of the 20% solution

4-x = 2 liters of the 10% solution

You really don't need 2 equations unless you want to designate

x = liters of 20% solution & y = liters of 10% solution

The the equations would be x + y = 4 and

{ 20x + 10y }/(x + y) = 15

You get the same answers!