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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?

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Answer:

50 gallos of 70%

100 gallons of 85%

Step-by-step 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     

  ------------------------------                 

                15y = 1500    

 Solve for y            15y = 1500                y = 100

x+100=150    x=50

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