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A spot has three kinds of activities to choose, there are canoeing, fishing, and swimming. People who chose canoeing are 15, 22 chose swimming, and 12 chose fishing. If 9 didn't choose anything, what is the minimum number of visitors?

I've tried to do this by adding all of them

x-9 = 22 - (a+b+d) + 12 - (a+c+d) + 15 - (b+c+d)

That left me with 52 = 2a + 2b + 2c + 3d

Now I don't know how to find the minimum value, or maybe I am wrong. Can anyone help me figure this out? Thanks

Godlixe
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  • Hint: To get the minimum number of visitors, you'll want as many as possible to choose multiple activities. – saulspatz Feb 08 '19 at 17:08

1 Answers1

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Consider a simpler case where there are only two activities, canoeing and swimming (still with $15$ and $22$ people respectively), and for the moment, ignore everyone who didn't choose an activity.

The number of visitors must be somewhere between $22$ and $37$. To get the minimum of $22$, the set of canoers must be a subset of the swimmers.

Can you see how to generalize this?

Théophile
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