Question

The last few years Casey has thrown an “arty party” where people get together and paint. Since people have very different experiences with paint, Casey has hired a professional to facilitate the party. The painting teacher charges per hour, and provides painting supplies at a per-attendee cost. Last year, 10 people came to the 2 hour party and Casey's bill was $350. The year before, it was 9 people for 2 hours and the bill was $335. Casey is going to ask this year's guests to chip in for the bill: $35 each. Casey worries whether this is in line with the previous years' expenses. It works fine for last year, but doesn't add up for the year before.

What is wrong with the following explanation of the discrepency?

"It was $350 for 10 people, so clearly $35 is the right price. For 9 people, Casey would only charge $315 total, saving her party-goers $20 each off the $335. What a bargain!"

Indicate clearly a mistake. Make sure to explain (quantitatively) how much of a difference the mistake actually makes. What happens if her guests ask for the $20 discount?

Answer 1

Casey is going to ask this year's guests to chip in for the bill is $35 each.

If there are 10 guests this year, then Casey will charge $(35×10) = $350.

If there are 9 guests this year, then Casey will charge $(35×9) = $315.

Here, Casey have to pay $350 for 10 people and $335 for 9 people.

That means for 9 people, Casey will pay $20 extra.

Therefore, for 9 people, Casey would pay $335 total, giving $20 extra for $335. What a loss!

The mistake actually makes a difference of $(20+20) ,i.e., $40.

If her guests ask for the $20 discount, then Casey have to pay $40 extra in total.