A chemical company makes two brands of antifreeze. The first brand is 55% pure antifreeze, and the second brand is 80% pure antifreeze. In order to obtain 170 gallons of a mixture that contains 65% pure antifreeze, how many gallons of each brand of antifreeze must be used?

  102 gallons of 55% antifreeze

  68 gallons of 80% antifreeze

Step-by-step explanation:

55% antifreeze:   x

80% antifreeze:   y

x + y = 170                        ===>  -.55(x + y = 170)   ===>   -.55x - .55y = -93.5

.55x + .80y = .65(170)      ===>                                          .55x + .80y = 110.5      

add the two equations to eliminate a variable:                        0.25y = 17

divide by 0.25 to isolate y:                                                               y = 68

substitution to find x:    

  x + y = 170

  x + 68 = 170

          x = 102