SOLUTION: A chemical company makes two brands of antifreeze. The first brand is 70 % pure antifreeze, and the second brand is 95 % pure antifreeze. In order to obtain 140 ga

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: A chemical company makes two brands of antifreeze. The first brand is 70 % pure antifreeze, and the second brand is 95 % pure antifreeze. In order to obtain 140 ga      Log On


   

Question 1112892: A chemical company makes two brands of antifreeze. The first brand is
70
%
pure antifreeze, and the second brand is
95
%
pure antifreeze. In order to obtain
140
gallons of a mixture that contains
80
%
pure antifreeze, how many gallons of each brand of antifreeze must be used?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The desired percentage of the mixture, 80, is 2/5 of the way from 70 to 95. (95-70 = 25; 80-70 = 10; 10/25 = 2/5)

That means 2/5 of the mixture must be the 95% antifreeze.

95% antifreeze: 2/5 of 140 gallons = 56 gallons
70% antifreeze: 3/5 of 140 gallons = 84 gallons

Answer: 56 gallons of 95%, 84 gallons of 70%

or you can use the much more difficult traditional algebraic solution method:

Let x be the number of gallons of 95% antifreeze
Then 140-x = number of gallons of 70% antifreeze

The 140 gallons of the mixture is 80% antifreeze:
.95%28x%29%2B.70%28140-x%29+=+.80%28140%29

A relatively easy equation to solve; but far more work than is required by the first method....