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Square Dance Partners, Trip Budget

Date: 6/30/96 at 17:30:27
From: Anonymous
Subject: Square Dance, Budget Trip

1. Sally invited seventeen guests to her party. When it came to the 
square dance, she assigned each guest a number from 2 through 18, 
keeping one to herself. Everyone had to have a partner so that the 
sum of each couple's number was a perfect square. What was the number 
of Sally's partner?

2. Mary budgeted $31 a day for her trip. With two days remaining, she 
had only $38 left and thus far had overspent $4 per day. How much did 
she take on her trip? How long had she planned to be traveling? How is 
she going to finish her trip, or will she be able to do so? 

Date: 7/1/96 at 8:12:21
From: Doctor Anthony
Subject: Re: Square Dance, Budget Trip

Dance Problem: 
The pairings are (18,7), (17,8), (16,9), (15,1), (14,2) (13,3), 
(12,4), (11,5), (10,6)

So Sally's partner was number 15.

Mary's Trip:
Let x = number days she planned for the holiday
 31*x = money she took with her.
She had actually spent 31+4 = $35 each day for (x-2) days. She had 
spent 35(x-2) and had only $38 left

So  31*x - 35(x-2) = 38
          -4x + 70 = 38
               -4x = -32  and so x = 8

She took 31*8 = $248  on the trip. She planned to travel for 8 days.
With $19 per day for the last two days she had better live on bread 
and water.

-Doctor Anthony,  The Math Forum
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