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?
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.
Let's start by finding the total number of jellybeans in the full bag.
Mike took 1/3 of the jellybeans, and Zac took 1/2 of the jellybeans.
So, the fraction of jellybeans left in the full bag is 1 - (1/3 + 1/2) = 1 - (2/6 + 3/6) = 1 - (5/6) = 1/6.
Now let's find the number of jellybeans Kary took.
Since Kary took what was left, she took 1/6 of the jellybeans in the full bag.
Now, we need to figure out how many jellybeans each friend had initially.
Let's assume the number of jellybeans in the full bag is x.
Mike initially had (1/3 * x), and he ate 1/2 of his jellybeans.
So, the number of jellybeans Mike has now is (1/2 * (1/3 * x)) = (1/6 * x).
Zac initially had (1/2 * x), and he also ate 1/3 of his jellybeans.
So, the number of jellybeans Zac has now is (2/3 * (1/2 * x)) = (1/3 * x).
Now, we are given that Mike and Zac together have a total of 45 jellybeans.
So, (1/6 * x) + (1/3 * x) = 45.
Combining the like terms, we get (1/6 + 1/3) * x = 45.
Simplifying, we get (3/6 + 2/6) * x = 45.
So, (5/6) * x = 45.
Dividing both sides by 5/6, we get x = (45) / (5/6).
Simplifying further, we get x = (45) * (6/5).
x = 54.
Therefore, there were 54 jellybeans in the full bag.
Since Kary took 1/6 of the jellybeans, she ate (1/6 * 54) = 9 jellybeans.
Therefore, Kary ate 9 jellybeans.