What's the solution to this problem? I have been struggling with it for quite a while.

Question

A chemical company makes two brands of antifreeze. The first brand is 70%

 pure antifreeze, and the second brand is 85%

 pure antifreeze. In order to obtain 90

 gallons of a mixture that contains 75%

 pure antifreeze, how many gallons of each brand of antifreeze must be used?

Answer 1

Let's call the first brand A and the second brand B.

Brand A will contribute x gallons to the final mixture and Brand B will contribute y gallons. This means the total mixture of 90 gallons can be represented as follows:

x + y = 90

Since brand A is 70% pure antifreeze the amount of pure antifreeze in gallons in the final mixture coming from brand A will be 0.7x

Since Brand B is 85% antifreeze the amount of pure antifreeze in the final mixture coming from brand B will be 0.85y

Since the final mixture is 75% and the total is 90 gallons we can represent it mathematically in terms of the percentages of A and B as follows:

0.7x + 0.85y = 0.75x95 = 67.5

Now we can use these two equations to solve for x and y.

x + y = 90

x = 90 - y

0.7x + 0.85y = 67.5

0.7(90-y) + 0.85y = 67.5

63 - 0.7y + 0.85y = 67.5

0.15y = 4.5

y = 30 --> 30 gallons of antifreeze B used in final mixture

x = 90 - y

x = 90 - (30)

x = 60 --> 60 gallons of antifreeze A used in final mixture