Question 1119385

I tried looking at some examples but i'm still confused. Can someone help please? thank you. 

A chemical company makes two brands of antifreeze. The first brand is 20% pure antifreeze and the second brand is 70% pure antifreeze. In order to obtain 180 gallons of a mixture that contains 40% pure antifreeze, how many gallons of each brand of antifreeze must be used?
<pre>Let amount of 20% antifreeze be T
Then amount of 70% antifreeze to mix = 180 - T (amount of 20%, plus amount of 70% MUST equal 180 gallons)
We then get: .2T + .7(180 - T) = .4(180)
.2T + 126 - .7T = 72
.2T - .7T = 72 - 126
- .5T = - 54
T, or amount of 20% to mix: {{{highlight_green(matrix(1,4, (- 54)/(- .5), "=", 108, gallons))}}}
Amount of 70% antifreeze to mix: {{{highlight_green(matrix(1,4, 180 - 108, "=", 72, gallons))}}}