Solving a percent mixture problem using a system of linear equations

Question

A chemical company makes two brands of antifreeze. The first brand is 35%

 pure antifreeze, and the second brand is 85%

 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?

Answer 1

.85x + .35(180-x) = .4(180)

.85x - .35x = .4(180) -.35(180)

.5x = .05(180) = 9

x = 9/.5 = 90/5 = 18 gallons of 85%

mixed with 180-18 = 162 gallons of 35%

yield a mixture of 180 gallons of 40%

35 is withiin 5 of 40

85 is within 45 of 40

you need 45/5 = 9 times as much 35% as 85%

162/18 = 9

but you want a "system of equations" as the answer

so try 2 equations, 2 unknowns, with x=gallons of 85% and y= gallons of 35%

.85x + .35y = .4(180)

and

y = 180-x

That's probaby the answer you want