Chemical Algebra System of Equations Question

Question

A chemical company makes two brands of antifreeze. The first brand is 65%

 pure antifreeze and the second brand is 90%

 pure antifreeze. In order to obtain 170

 gallons of a mixture that contains 70%

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

Answer 1

.9x + .65(170-x) = .7(170)

.9x -.65x = .7(170) - .65(170) = .05(170) = 8.5

.25x = 8.5

x = 8.5/.25 = 34 gallons of 90%

170-x = 136 gallons of 65%

.9(34) + .65(136) = 30.6 + 88.4 = 119 = .7(170)

another way to solve the problem:

70 is within 5 of 65

90 is within 20 of 70

you need 20/5 = 4 times as much 65%

1/5 of 170 = 34 gallons of 90%

4/5 of 170 = 136 gallons of 65%

It's similar to a weighted average such as grades

You need a 70 average in 170 tests

how many 65's and how many 90's would give you a 70 average?

90x + 65(170-x) = 70(170)

90x -65x = 70(170) -65(170) = 5(170)

25x = 850

x = 850/25 = 34 90's

170-x = 136 65's