Question

Three friends share a full bag of jellybeans. Mike took 1/3 of the jellybeans in the full bag, Zac took 1/2 of the jellybeans in the full bag 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 and Zac now have a total of 45 jellybeans together, how many jellybeans did Kary eat?

Answer 1

Kary ate 15 jellybeans.

Explanation:

Let x be the total number of jellybeans,

According to the question,

Jellybeans taken by Mike =
`(x)/(3)`

Jellybeans taken by Zac =
`(x)/(2)`

Jellybeans taken ( or eaten ) by Kary = Remaining jellybeans

`=x-(x)/(3)-(x)/(2)`

`=(6x-2x-3x)/(6)`

`=(x)/(6)`

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 =
`(x)/(6)+(x)/(6)`

`=(2x)/(6)`

`=(x)/(3)`

Remaining jellybeans contained by both Mike and Zac =
`((x)/(3)+(x)/(2))-(x)/(3)`

`=(x)/(2)`

Again according to the question,

`(x)/(2)=45`

`\implies x=90`

Hence, the jellybeans eaten by Kary =
`(90)/(6)` = 15