Question

A chemical company makes two brands of antifreeze. The first brand is 30% pure antifreeze, and the second brand is 75% pure antifreeze. In order to obtain 30 gallons of a mixture that contains 60% pure antifreeze, how many gallons of each brand of antifreeze must be used?

Answer 1

Let x = amount of 45% antifreeze

Let y = amount of 70% antifreeze

EQUATION 1: x + y = 150 (total of 150 gallons mixed)

EQUATION 2: .45x + .75y = .55(x + y)

Simplify and solve the system of equations

Multiply second equation by 100 on both sides to remove the decimals

45x + 75y = 55(x + y)

Combine like terms

45x + 75y = 55x + 55y

45x - 55x + 75y - 55y = 0

-10x + 20y = 0

Now we have the following system of equations:

x + y = 150

-10x + 20y = 0

Multiply the first equation by -10 to get opposite coefficients for x; add the equations to eliminate x

10x + 10y = 1500

-10x + 20y = 0

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30y = 1500

Solve for y

30y = 1500

y = 50

Since the total mixed gallons is 150, x = 150 - 50 = 100

So we need 100 gallons of the 45% antifreeze and 50 gallons of the 70% antifreeze