Proof in the Pudding?

Question

The Browns have three children. mike, sarah, and april. mike said that he saw some pudding in the refrigerator and ate one-half of it. april said she saw some pudding in the refrigerator and said she ate one-third of it. sarah said she saw some pudding in the refrigerator and ate all of it! it turns out that each of the three children had the same amount of pudding. what actually happened?
can u please show me how to do this problem?

Answer 1

April ate 1/3 first- leaving 2/3 of the original amount but to Mike it was the only amount he saw, so he ate 1/2 of what was there 1/2 of 2/3 =2/6 which reduces down to 1/3. Than Sarah saw some the pudding and ate what was left of it- which since 1/3 & 1/3 of the origal amount had already been eaten- it left her with 1/3 of the original amount. Thus all 3 children ate 1/3 of the origal amount. April, Mike Sarah in that order. Gee I want some pudding now too! :)

Answer 2

Obviously, Sarah was the last one to eat any of the pudding, because she finished it off. If Mike ate half of what he saw, then he left half of what he saw, so he must have ate right before Sarah. April must have eaten first.

Notice that we couldn't have had Mike eat first. If there was "x" amount of pudding, then he would have eaten x/2, leaving x - x/2 = x/2. Then April would have eaten (1/3)(x/2) = x/6, which is less than what Mike ate. But we're told that they all had the same amount, so this couldn't have happened. This leaves the only other possible order as April, Mike, Sarah.

I suppose the simplest thing that could have happened was that there were three cups of pudding. April had one, then Mike had one, and Sarah had the last one. Regardless, if "x" was the original amount, then Sarah had x/3. Then Mike had (1/2)(x - x/3) = (1/2)(2x/3) = x/3. He ate just as much as he left behind so Sarah had x/3 too.

Answer 3

April was the first to eat the pudding, leaving 2/3 of the original amount. Mike ate next, taking 1/2 of what was there (or 1/3 of the original amount), leaving 1/3 of the original amount to be eaten by Sarah.

Answer 4

First, April saw the entire pudding, and ate 1/3, then Mike came by ate half of what was left which is 1/3, finally Sarah came by and ate the remaining 1/3

Answer 5

Since each child ate an equal amount of pudding, there must have been three equal portions.

Let the starting amount of pudding be 3x. For the problem to work, each kid must eat x.

The first kid must eat a third of 3x, leaving 2x behind.
The second kid must eat half of 2x, leaving x behind.
The third kid then eats x, leaving nothing behind.

Clearly, April was the first to the fridge, Mike was second, and Sarah was last.

Hope that helps!

Answer 6

april had her third first then mike had his half and the rest is one third for sarah to eat last.