Solving a percent mixture problem using a system of linear equations

Question

A chemical company makes two brands of antifreeze. The first brand is 30% pure antifreeze, and the second brand is 80% pure antifreeze. In order to obtain 90 gallons of a mixture that contains 70% pure antifreeze, how many gallons of each brand of antifreeze must be used?

First brand:

Second brand:

Answer 1

Let x = number of gallons of 30% type and y = number of gallons of 80% type

Then, x + y = 90 and 0.30x + 0.80y = 0.70(90)

x + y = 90

30x + 80y = 6300

-30x - 30y = -2700

30x + 80y = 6300

50y = 3600

y = 72 gal and x = 18 gal