Question

A chemical company makes two brands of antifreeze. The first brand is 35 percent pure antifreeze and the second brand is 85 percent pure antifreeze. In order to obtain 90 gallons of a mixture that contains 55 pure antifreeze how many gallons of each brand of antifreeze must be used

Answer 1

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)