For his chemistry experiment, Martin needs 3 liters of a 40% alcohol solution. The lab has two containers, one with 20% alcohol solution and the other with 50%

Question

For his chemistry experiment, Martin needs 3 liters of a 40% alcohol solution. The lab has two containers, one with 20% alcohol solution and the other with 50% alcohol solution. 

a.) Write a system of linear equations that you can use to determine how many liters of each type of alcohol solution Martin should combine to get 3 liters of a 40% alcohol solution. Be sure to define your variables.

b.) solve the system and determine how many liters of each type of alcohol solution Martin should combine. Show all your work.

Answer 1

Let x = the total amount of 20% solution needed

 

y = the total amount of 50% solution needed

 

x + y = 3 (the total volume of the combined solution)

 

Also, we know that the total concentration of the mixture can be expressed as

 

x(0.20) + y(0.50) = 3(0.40)      [I converted each of the percentages to decimals]

 

.20x + .50y = 1.2   (Multiply both sides by 100 to clear the decimals)

 

20x + 50y = 120

 

Now, solve the first equation for y

 

x + y = 3 or y = 3 - x

 

We can plug this into the second equation:

 

20x + 50(3 - x) = 120

20x + 150 - 50x = 120

-30x + 150 = 120

-30x = -30

x = 1

 

If x = 1, then y = 3 - x = 3 - 1 = 2

 

We need 1 L of 20% solution and 2 L of 50% solution