a certain automobile gas tank contains15 gallons 12% which is ethanol how much gasoline should be removed so that when replaced with pure ethanol there is 22% ethanol in gas tank?

To solve this problem, we need to calculate how much gasoline should be removed from the gas tank. Here's how you can do it:

Step 1: Determine the initial amount of ethanol in the gas tank.
Since the gas tank contains 15 gallons, and 12% of it is ethanol, we can calculate the initial amount of ethanol by multiplying 15 gallons by 0.12:
Initial ethanol = 15 gallons * 0.12 = 1.8 gallons

Step 2: Determine the amount of gasoline to be removed.
Let's assume we remove x gallons of gasoline from the tank. Since we are replacing it with pure ethanol, the ratio of ethanol to the total volume will be:
(Initial ethanol + x gallons of ethanol) / (15 gallons - x gallons of gasoline + x gallons of ethanol) = 22%

Step 3: Solve for x.
Using the equation from Step 2, we have:
(1.8 + x) / (15 - x + x) = 0.22

Simplifying the equation, we get:
(1.8 + x) / 15 = 0.22

Multiply both sides of the equation by 15 to eliminate the fraction:
1.8 + x = 15 * 0.22
1.8 + x = 3.3

Subtract 1.8 from both sides of the equation to isolate x:
x = 3.3 - 1.8
x = 1.5

So, you should remove 1.5 gallons of gasoline from the gas tank.