two equations

Question

How many gallons of a 10% salt solution must be mixed with 50 gallons of a 50% salt solution to obtain a 20% salt solution?

Answer 1

Let x = the number of gallons of 10% solution.

 

 

x + 50 would be the new volume of 20% solution.

 

The absolute amount of salt is the same before and after:

 

0.1x + 0.5(50) = 0.2(x + 50)

 

 

Solving for x,

 

0.1x + 25 = 0.2x + 10

 

0.1x = 15

 

x = 150 gallons.

 

 

Check: 0.1(150) + 0.5(50) = 40 gallons of salt

 

150 + 50 = 200 total gallons.

 

 

40/200 = 0.2 or 20%