I could just divide both sides by 0.05.That’s going to get me 12 liters.So we need to add 12 liters of the fuel station gasoline to our tank in order to get gasoline with a 20% concentration of ethanol.
We’re told a partially filled tank holds 30 liters of gasoline with an 18% concentration of ethanol. A fuel station is selling gasoline with a 25% concentration of ethanol. What volume in liters of the fuel station gasoline would we need to add to the tank to get gasoline with a 20% concentration of ethanol?
To figure this out, we need to consider how concentration relates to total volume, and calculate the volume of ethanol in the tank. We know the concentration is 18%, and the total volume is 30 liters, so 18% of 30 liters is equal to 5.4 liters of ethanol.
We need to find the volume of the fuel station gasoline we would need to add to the tank to get a 20% concentration. We can set this volume equal to v, and our 20% concentration is equal to the new volume of ethanol divided by the new total volume. Our new total volume is the 30 liters we started with plus the v liters we are adding, and our new volume of ethanol is the 5.4 liters we started with plus the volume of ethanol we are adding (0.25v).
We can solve this equation by multiplying both sides by 30 + v, and then subtracting 0.2v from both sides. This will leave us with 0.6 = 0.05v. Dividing both sides by 0.05 gives us the answer: 12 liters.
Therefore, we need to add 12 liters of the fuel station gasoline to our tank in order to get gasoline with a 20% concentration of ethanol. The result of 60 divided by 5 is 12 liters. To verify the new concentration, if 12 liters of this concentration are added to 30 liters of that concentration, it will result in a 20% concentration of ethanol. We are done.