Answer: To solve this problem, we can work backwards by finding the original amount of lemonade that Joe started with.
Let's assume the original amount of lemonade Joe started with is represented by "x" liters.
Joe sold 1/2 of the lemonade at lunch, which means he had (1/2)x liters remaining.
He then sold 3/4 of that remaining amount at breakfast, leaving (1 - 3/4) * (1/2)x = (1/4) * (1/2)x = (1/8)x liters.
Finally, he sold 1/3 of the remaining lemonade at dinner, which left him with (1 - 1/3) * (1/8)x = (2/3) * (1/8)x = (1/12)x liters.
According to the information given, Joe has 4 liters remaining. So, we can set up the equation:
(1/12)x = 4
To solve for x, we can multiply both sides of the equation by 12:
x = 4 * 12
x = 48
Therefore, Joe initially started with 48 liters of lemonade.