Sharon Spent $2 on a magazine; then she spent half of the rest of her money on shoes. She spent half of her remaining money on lunch. She has $12 left. How much did Sharon start with?

X= X+2+(a÷2)+(b÷2)+12

Thats correct?

since you don't define a,b it's hard to say.

You can check by plugging in the results you got to see whether they satisfy the equation you derived.

One thing that troubles me is that X vanishes from the equation if you subtract X from both sides.

Actually, the equation you wrote is not correct. Let's break down the problem and come up with the correct equation.

We are given that Sharon spent $2 on a magazine. Let's call the amount of money she had before spending as "x".

After spending $2 on the magazine, Sharon has "x-2" dollars left.

Then, she spent half of that remaining money on shoes. This means she spent (1/2) * (x-2) dollars on shoes.

After buying shoes, Sharon has (x-2) - (1/2) * (x-2) dollars remaining.

Next, she spent half of her remaining money on lunch. This means she spent (1/2) * [(x-2) - (1/2) * (x-2)] dollars on lunch.

After buying lunch, Sharon has [(x-2) - (1/2) * (x-2)] - (1/2) * [(x-2) - (1/2) * (x-2)] dollars left.

Finally, we are given that Sharon has $12 left. So we can set up the equation:

[(x-2) - (1/2) * (x-2)] - (1/2) * [(x-2) - (1/2) * (x-2)] = 12

Now, we can simplify this equation and solve for x to find out how much money Sharon started with.