System of equations

Question

A chemist currently has two solutions of sodium chloride. One solution has a 5% concentrate and the other has a 25% concentrate. The chemist needs to make 10 L of a 10% sodium chloride solution.

Let x = the amount of 5% solutions.

Let y = the amount of 25% solution.

How much of each solution does the chemist need to make?

Answer 1

Let x = the amount of 5% solutions.
Let y = the amount of 25% solution.

 

Mixture:

0.05x + 0.25y = 0.1(10L)

 

total volume:

x + y = 10L

 

rearrange total volume equation

x + y = 10

x = 10 - y

 

substitute this into the first equation for x and solve for y

 

0.05(10 - y) + 0.25y = 0.1(10)

 

distribute

 

0.5 - 0.05y + 0.25y = 1

0.5 + 0.2y = 1

0.2y = 1 - 0.5

0.2y = 0.5

y = 0.5/0.2

 

y = 2.5L

 

 

Go back and plug y into original total volume equation

x + y = 10L

 

x + 2.5L = 10L

x = 10L - 2.5L

 

x = 7.5L