x= amount of 35% anti freeze
y= amount of 85% antifreeze
We have to write a system of equations:
x + y = 90 (90 gallons mixed)
0.35x + 0.85y = 0.55 (x+y)
Solve the system:
x + y = 90
0.35x + 0.85y = 0.55 (x+y)
First, simplify the second equation:
0.35x+0.85y = 0.55x +0.55y
0..35x-0.55x +0.85y-0.55y= 0
-0.2x + 0.3y = 0
Now we have:
x + y = 90
-0.2x + 0.3y = 0
Multiply the first equation by 0.2, and then add the equations to eliminate x
0.2x+0.2y = 18
+
-0.2x + 0.3y= 0
_____________
0.5y= 18
Solve for y:
y= 18/0.5
y= 36 (second brand)
Replace y on any equation, and solve for x:
x + y = 90
x + 36 = 90
x= 90-36
x= 54 (first brand)
54 gallons (first brand)
36 gallons (second brand)