Using systems of two or three linear equations to answer.

Question

 

How do you setup the equations?

A diver wants to create a tank of air that contains 36% Oxygen by combining two sources. The first source contains 20% oxygen the second source contains 60% oxygen. What percent of each source will the diver need to put into the tank?

Answer 1

Let P1 be the percent from the 20% source which will contain an amount of oxygen equal to 0.2*P1

Let P2 be the percent from the 60% source which will contain an amount of oxygen equal to 0.6*P2

 

The sum of the percentages used must be 1 (=100%) so one equation is P1 + P2 = 1

 

The total amount of oxygen in the combination must be 36% of the total amount used (which is 1) so the second equation is  

0.2*P1 + 0.6*P2 = 0.36*1  

 

Once you solve make sure to convert the decimal answer back into a percentage.