Question 517618
Solution A
Amount = x 
Concentration =35% =0.35

Solution B
Amount = 130-x
Concentration =85% = 0.85

Final Solution
Amount =130 
Concentration =55%=0.55

[Amount Solution A * Concentration A] + [Amount Solution B * Concentration of B] = Amount of Final * Concentration of Final
0.35x+(130-x)0.85=130*0.55
0.35x+110.5-0.85x=71.5
-0.5x=71.5-110.5
-0.5x=-39
-0.5x/-0.5=-39/-0.5
x=78
Solution A
Amount = 78 gallons
Concentration =35% =0.35

Solution B
Amount = 130-x=130-78=52 gallons
Concentration =85% = 0.85

We have to mix 78 gallons of of oil with 35% hydrocarbons and 52 gallons of oil with 85% hydrocarbons to get 130 gallons of oil with 55% hydrocarbons.