Question

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

130

gallons of a mixture that contains

70%

pure antifreeze, how many gallons of each brand of antifreeze must be used?

Answer 1

9514 1404 393

Answer:

• 52 gallons of 55%
• 78 gallons of 80%

Explanation:

Let x represent the quantity of 80% solution. Then the quantity of 55% solution is (130-x) and the total amount of antifreeze in the mix is ...

0.55(130 -x) +0.80(x) = 0.70(130)

0.25x +71.5 = 91 . . . simplify

0.25x = 19.5 . . . . . . subtract 71.5

x = 78 . . . . . . . . . . . divide by 0.25; amount of 80%

130-78 = 52 . . . . amount of 55%

52 gallons of the 55% brand, and 78 gallons of the 80% brand must be used.