solving a percentage mixture using a system of linear equations

Question

A chemical company makes two brands of antifreeze. The first brand is 40% pure antifreeze, and the second brand is 90% pure antifreeze. In order to obtain 120 gallons of a mixture that contains 80% pure antifreeze, how many gallons of each brand of antifreeze must be used?

Answer 1

F+N = 120

40F + 90N = 120(80)= 9600

4F + 9N =960

F=120-N

4(120-N) +9N =960

480 -4N + 9N = 960

5N = 480

N=480/5 = 96 gallons of 90%

F = 120-96 = 24 gallons of 40%

to get 120 of 80%