The question is:

A Woman is selling an (X) amount of Oranges

The first time she sold half of the total Oranges and half of an Orange.

The second time she sold half of what is left of the Oranges and also half of an Orange.

The third time she sold half of what's left of the Oranges and half of an Orange. After that all her oranges are sold.

What is the total numbers of Oranges?

I'm not sure how to express that in an algrebraic expression and go about solving it.

Do you have the correct information?

If she sold three half-oranges, she will still have at least a half-orange left. So how could it be "that all her oranges are sold"?

Please repost. Thanks for asking.

To solve this problem, let's break it down step by step using algebraic expressions.

Let's assume the total number of oranges is represented by the variable "X."

According to the problem statement:
- The first time she sold half of the total oranges and half of an orange, which can be expressed as (X/2) + 0.5.
- After the first sale, the remaining oranges can be calculated as the difference between the initial total and the first sale: X - [(X/2) + 0.5] = (X/2) - 0.5.
- The second time she sold half of what is left of the oranges and half of an orange, which can be expressed as [(X/2) - 0.5]/2 + 0.5.
- After the second sale, the remaining oranges can be calculated as the difference between the remaining oranges after the first sale and the second sale: (X/2) - 0.5 - {[(X/2) - 0.5]/2 + 0.5} = (X/4) - 0.5.
- The third time she sold half of what's left of the oranges and half of an orange, which can be expressed as [(X/4) - 0.5]/2 + 0.5.
- Finally, after the third sale, all her oranges are sold, so the remaining oranges would be 0.

Now we can set up the equation to solve for X:

(X/4) - 0.5 - {[(X/4) - 0.5]/2 + 0.5} = 0.

To solve this equation, we can simplify and combine like terms:

(X/4) - 0.5 - (X/8) + 0.25 - 0.5 = 0.

Combining the terms, we get:

(2X - 4 - X + 2 - 4)/8 = 0.

Simplifying further:

X - 6 = 0.

Now, solve for X:

X = 6.

Therefore, the total number of oranges is 6.