Friday, April 15, 2016

Spring 2016 POTW #5: Check (Your Work), Please!

Solutions due by Sunday, April 24, 2016.

This is the final POTW of the year! We will be awarding prizes for yearlong standings at an Emmanuel Math Department event at 4:30 pm on Thursday, April 28, 2016 (which is also Senior Distinction Day). At the same time, we will be inducting members of the graduating class into the mathematics honor society Pi Mu Epsilon. Emmanuel folks, please join us in celebrating the outstanding achievements of our seniors and you, the puzzlers!

The 6 members of the Emmanuel Math Department recently went out to a celebratory dinner. When it came time to pay the bill, they discovered a few curiosities:

  • Everyone except Brendan owed exactly the same amount for their meal.
  • Brendan was an extravagant spender: His meal cost $10 more than twice the average of everyone's cost.
  • Meanwhile, each other person's meal cost $10 more than half the average of everyone's cost.
What was the total bill for everyone, and how much did Brendan's meal cost?

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