Final answer:
6000 gallons of 8% ethanol gasoline need to be added to 2000 gallons of ethanol-free gasoline to get a mixture that is 6% ethanol.
Step-by-step explanation:
To determine how many gallons of 8% ethanol gasoline must be added to 2,000 gallons of gasoline with no ethanol to achieve a 6% ethanol mixture, we can set up an equation based on the principle that the amount of ethanol in the final mixture is the sum of the amounts of ethanol in the individual components.
Let x be the number of gallons of 8% ethanol to be added. The equation is: 0.08x = 0.06(2000 + x). Rearranging the equation to solve for x, we get: 0.08x - 0.06x = 0.06(2000). Simplifying further, 0.02x = 120, which gives us x = 120 / 0.02, resulting in x = 6000.
Therefore, you need to add 6000 gallons of 8% ethanol gasoline to 2000 gallons of ethanol-free gasoline to get a mixture that is 6% ethanol.