Question

A chemical company makes two brands of antifreeze. The first brand is 70% pure antifreeze, and the second brand is 85% pure antifreeze. In order to obtain 150 gallons of a mixture that contains 80% pure antifreeze, how many gallons of each brand of antifreeze must be used?

Answer 1

50 gallos of 70%

100 gallons of 85%

Explanation:

x = amount of 70% antifreeze

y = amount of 85% antifreeze

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

EQUATION 2: .70x + .85y = .80(x + y)

Multiply second equation by 100 on both sides to remove the decimals 70x + 85y = 80(x + y)

70x + 85y = 80x + 80y (distributive)

70x - 80x + 85y - 80y = 0

-10x + 5y = 0

Now we have the following system of equations:

x + y = 150

-10x +5 y = 0

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

10x + 10y = 1500

-10x + 5y = 0

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15y = 1500

Solve for y 15y = 1500 y = 100

x+100=150 x=50