A petroleum company has two different sources of crude oil. The first source provides crude oil that is 65% hydrocarbons, and the second one provides crude oil that is 90% hydrocarbons. In order to obtain 80 gallons of crude oil that is 75% hydrocarbons, how many gallons of crude oil must be used from each of the two sources?

Make a system of two equations, with variable x = number of a gallons from the first source and y the number of gallons from the second one.

(1) x + y = 80 gallons

0.65 x + 0.90y = 0.75*80

(2) 0.65x + 0.90y = 60

From (1) y = 80 - x

Substitute in (2) 0.65x + 0.90 (80 - x) = 60

0.65x + 72 - 0.90x = 60

0.25x = 12

x = 48 gallons

y = 80 - 48 = 32 gallons

Answer: 48 gallons of the first source and 32 gallons from the second one.