A petroleum company has two different sources of crude oil. The first source provides crude oil that is 35% hydrocarbons, and the second one provides crude oil that is 60% hydrocarbons. In order to obtain 120 gallons of crude oil that is 55% hydrocarbons, how many gallons of crude oil must be used from each of the two sources?
work with the amount of hydrocarbons present in each part:
.35x + .6(120-x) = .55*120
x = 24
so, 24 gals of 35%, and 96 gals of 60%
25,8
you left the most garbage explanation I may have seen in my entire life. Save your hands, and don't post unless its worth reading.
To solve this problem, we can use a method called the "Mixture" or "Alligation" method. This method involves finding the weighted average of the two sources of crude oil to obtain the desired percentage of hydrocarbons.
Let's assume x gallons of crude oil are used from the first source, which is 35% hydrocarbons. This means that the remaining quantity, (120 - x) gallons, must come from the second source, which is 60% hydrocarbons.
Now, we need to find the weighted average of hydrocarbons to achieve the desired 55% hydrocarbons in the final mixture.
The weighted average is calculated as follows:
(35% * x) + (60% * (120 - x)) = 55% * 120
Let's solve this equation to find the value of x:
0.35x + 0.60(120 - x) = 0.55 * 120
0.35x + 72 - 0.60x = 66
-0.25x = -6
x = -6 / -0.25
x = 24
Therefore, 24 gallons of crude oil from the first source (35% hydrocarbons) and (120 - 24 = 96) gallons from the second source (60% hydrocarbons) must be used to obtain 120 gallons of crude oil that is 55% hydrocarbons.