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 Check out our web site! http://mathforum.org/dr.math/
Search the Dr. Math Library:
Ask Dr. MathTM
© 1994- The Math Forum at NCTM. All rights reserved.