Applications of systems of euations?

Question

How many gallons of 35  % alcohol solution and 50  % alcohol solution must be mixed to get 6  gallons of 40  % alcohol solution?

Answer 1

Let the volume of the first solution (35%) be x and the second (50%) be y.

 

Total volume = 6 gallons so

x + y = 6    <- eq1 for total volume

 

For the amount of alcohol..

0.35 of x added with 0.5 of y gives 0.4 of 6 so

 

0.35x + 0.5y = 0.4*6    <- for amount of alcohol

0.35x + 0.5y = 2.4        <- eq2

 

substitue x from eq1 in eq2

0.35(6 - y) + 0.5y = 2.4

2.1 - 0.35y + 0.5y = 2.4

0.15y = 0.3

y = 2 gallons

 

x = 6 - y = 6 - 2 = 4 gallons.