Mary had some M&M candy. She ate one, then gave half of the remaining candy to Bill. She ate another candy, then gave 1/3 of the remaining to Edie, leaving 6. How many did she give away to Bill and Edie?

40???

If there are 6 left after Mary has given a third to Edie then there must have been 9 to start with and she gave 3 to Edie.

Before she ate one there must have been 10 sweets.
So after giving half to Bill she has 10 left there must have been 20 to start with and she gave 10 to Bill.

Thus she gave 3+10 = 13 to Bill and Edie.

Just check my maths. No idea how you got to 40.

oops, i misread the problem

Don't forget the one she ate before she gave 1/2 to Bill. I got that she started with 21.

"Don't forget the one she ate before she gave 1/2 to Bill. I got that she started with 21" But that is not the question, the question asks "how many she gave to Bill and Edie?", NOT "how many did she start with?"

Thank you. I can follow the solution quite easily as explained, but I could never have come up with the solution from scratch other than just starting with numbers and trial and error. So how do you begin such a problem?

To solve this problem, we can work backward from the final statement. We are given that Mary has 6 M&M candies left after giving some to Edie. Let's call the number of candies Mary had before giving any away as "x."

First, Mary ate one candy, so we subtract 1 from x: x - 1.

Next, Mary gave half of the remaining candies to Bill. That means she gave (x - 1) / 2 candies to Bill.

After giving some to Bill, Mary ate another candy, so we subtract 1 from the remaining candies given to Bill: (x - 1) / 2 - 1.

Finally, she gave 1/3 of the remaining to Edie, which can be expressed as (x - 1) / 2 - 1 - (1/3) * ((x - 1) / 2 - 1).

According to the problem, the above expression should equal 6. Now, we can solve the equation to find the value of x and calculate how many candies Mary gave away to Bill and Edie.

Once we have the value of x, we can calculate the number of candies Mary gave to Bill by substituting x back into (x - 1) / 2, and the number of candies she gave to Edie by substituting x into (1/3) * ((x - 1) / 2 - 1).