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?

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slicergiza slicergiza · Answer 1 · 2019-08-07T11:31:14+02:00

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 = [tex]\frac{x}{3}[/tex]

Jellybeans taken by Zac = [tex]\frac{x}{2}[/tex]

Jellybeans taken ( or eaten ) by Kary = Remaining jellybeans

[tex]=x-\frac{x}{3}-\frac{x}{2}[/tex]

[tex]=\frac{6x-2x-3x}{6}[/tex]

[tex]=\frac{x}{6}[/tex]

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 = [tex]\frac{x}{6}+\frac{x}{6}[/tex]

[tex]=\frac{2x}{6}[/tex]

[tex]=\frac{x}{3}[/tex]

Remaining jellybeans contained by both Mike and Zac = [tex](\frac{x}{3}+\frac{x}{2})-\frac{x}{3}[/tex]

[tex]=\frac{x}{2}[/tex]

Again according to the question,

[tex]\frac{x}{2}=45[/tex]

[tex]\implies x=90[/tex]

Hence, the jellybeans eaten by Kary = [tex]\frac{90}{6}[/tex] = 15