Question

3 friends share a fullbag of jellybeans. Mike took 1/3 of the jellybeans in the full bag ,Zac took 1/2 of the jellybeans in the fullbag and Kary took what was left. Mike ate 1/2 of his jellybeans, Zac ate 1/3 of his jellybeans and Kary ate all of hers. If Mike & zac now have a total of 45 jellybeans together,
howmany jellybeans did Kary eat?

Answer 1

Let's start by figuring out how many jellybeans were in the full bag.

Mike took 1/3 of the jellybeans, so 2/3 of the jellybeans were left.
Zac then took 1/2 of the remaining jellybeans, which means he took 1/2 * 2/3 = 1/3 of the original full bag.
That means Kary took the remaining 2/3 - 1/3 = 1/3 of the original full bag.

Now let's find out how many jellybeans Mike and Zac each took.

If Mike took 1/3 of the full bag and ate 1/2 of that, he has 1/2 * 1/3 = 1/6 of the full bag left.

If Zac took 1/3 of the full bag and ate 1/3 of that, he has 1/3 * 1/3 = 1/9 of the full bag left.

Together, Mike and Zac have 1/6 + 1/9 = 5/18 of the full bag.

We know that this equals 45 jellybeans, so let's set up an equation:

5/18 * full bag = 45

Solving for the full bag:

full bag = 45 * 18/5 = 162 jellybeans

Now we can figure out how many jellybeans Kary ate.

Kary took 1/3 of the full bag, which means she took 1/3 * 162 = 54 jellybeans.

And we know that she ate all of hers, so Kary ate 54 jellybeans.