Answer:
Kary ate 15 jellybeans.
Step-by-step explanation:
Let x be the total number of jellybeans,
According to the question,
Jellybeans taken by Mike = ![\frac{x}{3}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B3%7D)
Jellybeans taken by Zac = ![\frac{x}{2}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D)
Jellybeans taken ( or eaten ) by Kary = Remaining jellybeans
![=x-\frac{x}{3}-\frac{x}{2}](https://tex.z-dn.net/?f=%3Dx-%5Cfrac%7Bx%7D%7B3%7D-%5Cfrac%7Bx%7D%7B2%7D)
![=\frac{6x-2x-3x}{6}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B6x-2x-3x%7D%7B6%7D)
![=\frac{x}{6}](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bx%7D%7B6%7D)
Now, Mike ate 1/2 of his jellybeans, Zac ate 1/3 of his jellybeans,
So, the total jelly beans eaten by both Mike and Zac = ![\frac{x}{6}+\frac{x}{6}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B6%7D%2B%5Cfrac%7Bx%7D%7B6%7D)
![=\frac{2x}{6}](https://tex.z-dn.net/?f=%3D%5Cfrac%7B2x%7D%7B6%7D)
![=\frac{x}{3}](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bx%7D%7B3%7D)
Remaining jellybeans contained by both Mike and Zac = ![(\frac{x}{3}+\frac{x}{2})-\frac{x}{3}](https://tex.z-dn.net/?f=%28%5Cfrac%7Bx%7D%7B3%7D%2B%5Cfrac%7Bx%7D%7B2%7D%29-%5Cfrac%7Bx%7D%7B3%7D)
![=\frac{x}{2}](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bx%7D%7B2%7D)
Again according to the question,
![\frac{x}{2}=45](https://tex.z-dn.net/?f=%5Cfrac%7Bx%7D%7B2%7D%3D45)
![\implies x=90](https://tex.z-dn.net/?f=%5Cimplies%20x%3D90)
Hence, the jellybeans eaten by Kary =
= 15