Three Friends     Three friends have a tradition of buying each other a New Year’s gift each year. Each person is bought a gift by the other two friends who split the cost equally. Therefore, friend A and friend B each pay half the cost of the gift for friend C, friend B and friend C each pay half the cost of the gift for friend A, and friend C and friend A pay half the cost of the gift for friend B. The final rule for this gift giving process is that the gifts are purchased together on the same day where each person spends all the money they bring to the event. If friend A brings $50, friend B brings $58, and friend C brings $62, what are the prices for each of the three gifts?
March 27, 2006
Past Problems
	E-mail Solutions to: pow@umassd.edu
	Correct Solutions
	Roland Vyncke. Bruges, Belgium Eugene Roytman. New York, NY Tim Poe. Austin, TX Radu Ionescu. Montreal, Quebec, Canada Jerome Cherry. Mundare, Alberta, Canada Dennis Muniz. Commack, NY Gary Brensike. Fairfax, VA Wenlin Fan. Mountain Top, PA Aristides Kyriakakis.  Thessaloniki,  Greece Jerrold Greenberg. New York, NY Bob Mitchell. Normal, IL Nikki Tan, Southridge School, Surrey, BC, Canada Dmitry Vagner. Ranney School, Tinton Falls, NJ Andy Drabic. Archbishop Hoban High School, Akron, OH Daniel Senécal. Collège Jean-Eudes, Montréal, Québec, Canada Lisa Schechner. Schreiber HS, Port Washington, NY Farid Lian, Uniatlantico, Barranquilla-Colombia Shena Jagnarain. Gwinnett County Public Schools, Duluth, GA Gopal Kumar. Hendrik Salomons. Arapoti, Brazil Greg LaCroix. Somerdale, NJ Craig Sidell. New York, NY Jansen Teo. Nanyang Technological University, Singapore Emil Lalov. Mathematical High School, Pleven, Bulgaria Christopher Thomas. New York, NY Coman Daniel. Romania,Braila Alexey Vorobyov. Siraj Iqbal. Miami Killian Senior High, Miami, FL John Molokach. East Carteret High School, Beaufort, NC Phillip Ai. Hammarskjold Middle School, East Brunswick, NJ Charles Keebaugh. Colorado Springs, CO Daniel Acosta-Kane. Miami Killian Senior High School, Miami, FL Sagar Patel. Brookstone School, Columbus, GA Phillip Ai.  Hammarskjold Middle School, East Brunswick, NJ Korynn Camara.  Freetown/Lakeville Middle School, Lakeville, MA Kristy Chang. South Pasadena Middle School, South Pasadena, CA Nhut Tran. Barton Secondary School, Hamilton, ON ,Canada Sarah Chen. Marie Curie Middle School, New York, NY Graham Anderson. Faith Lutheran College, Plainland, Australia Dan Baum. James Madison Memorial High School, Madison, WI Albert Zhou.  Scott Middle School, Lincoln, NE Katherine Wang. South Pasadena Middle School, South Pasadena, CA Bilyana Tzolova . EPWE, PA Seth Flowers. Parkersburg High School. Parkersburg, WV Andrew Bennett. Honey Island Elementary, Slidell, LA Svadharma Keerthi. South Pasadena Middle School, CA Kunal Singh. Kendriya Vidyalaya Happy Valley Shillong, India Tiffany Chen. South Pasadena Middle School, South Pasadena, CA Michael Vishevnik. Michelle Lam. South Pasadena Middle School, South Pasadena, CA John Song. White Station HS, Memphis, TN James Kawakami. South Pasadena Middle School, CA Ken Tyburski.  Chatham Hall, Chatham, VA Brian Hetrick. UNH, Durham, NH Stephen Farver.  PJ23 High School, Katy, TX Topher Conlan. University of Florida, Gainesville, FL Frank McGartland. Saskatoon, SK., Canada Melissa Chaffin. University of Georgia, Athens, GA Ross Pacheco.  Hastings Middle School, Fairhaven, MA Richard S. Levine.  Clearwater, Florida Renee Sears. Hart High School, Newhall, Ca Nick Taylor.  Tacoma, WA Allysha Silva.  Hastings Middle School, Fairhaven, MA Danny Gordon.  Columbus , GA Randy Hargis Minseon Shin.  IL Ryan McElhinny. Arrowhead High School, Hartland, WI Iver Meng. South Pasadena Middle School, South Pasadena, CA Daniel Pyon. South Pasadena Middle School, South Pasadena, CA Rin Sone. South Pasadena Middle School, CA Abhijeet Singh. Rai Foundation Colleges, Mumbai, India Kevin Dong. Westlake Elementary School, Santa Cruz, CA Willie Dong, Westlake Elementary School, Santa Cruz, CA Mak Amanda. S1 Unity, CHIJ St. Nicholas Girls' School, Singapore. Er Cheryl. CHIJ St. Nicholas Girls' School, Singapore, Jason Wetherington. Brooksville, FL Magdy Essafty. Egypt Soo-hyun Lee. Sauk Centre HS, Sauk Centre, MN Mason Bates. Creekwood Middle School, Kingwood, TX Jennifer Sailor. Osceola Middle School, Ocala, FL Andrew Sailor. Osceola Middle School, Ocala, FL Shareef Bacchus. Hilsman Middle School, Athens GA Drew Wolfard. Kea'au Middle School, Kea'au, HI Brittany Cole. Dartmouth High School, Dartmouth MA Lauren Champion. Brookstone School, Columbus, GA Fabian Moa. NIIT College, Kuching, Sarawak, Malaysia Daniel Bernucci. Collège Jean-Eudes, Montreal, Quebec, Canada Laura Felder.  Creekwood Middle School, Kingwood, TX Slayton Gilmore.  Brookstone School, Columbus, GA Lusha Zhou.  Qingdao,, China Bill Croughan.  Episcopal School of Acadiana, Cade, LA Gavin Tse. Pasadena Middle School, South Pasadena, CA Jake Daniels. Beck Middle School, Cherry Hill, NJ Matthew Wong. South pasadena Middle School, South Pasadena, CA Aashrita Mangu. South Pasadena Middle School, South Pasadena, CA Kivi Geller. Beachwood, OH Luan Nguyen. San Jose, CA , Sheppard Middle School Jonathan Uesato. Milpitas Christian School, San Jose, CA Skyler Weaver. Oregon State University, Corvallis, OR Garrett Hix. Brookstone School, Columbus, GA Patti O'Connell. Blessed Teresa School, Ferguson, MO Paul Rice. OBMS, Ormond Beach, FL Mark Spanier. Sauk Centre HS, Sauk Centre, MN Albert Soh.  Eldorado K-8, Superior, CO Mike Osterfoss. Moore, SC Brett Grady. Sending from Our Lady of Sorrows, Toronto, Ontario, Canada Rebecca Greenberg. Beck Middle School Annelise Broussard. Creekwood Middle School, Kingwood, TX Liza. MA Alstyne Gravlee. St.Luke School, Columbus, GA Sarah Bartley. Rye Junior High School, Rye, NH Alan Leung. Mississippi School for Mathematics and Science, Columbus, MS Jungchando Sehwa. Girls High School, Seoul, Korea Bill Freeman. Kingwood, TX Brianna Loo. South Pasadena Middle School, South Pasadena, CA Steph Lochowski. Wilcox Tech, Meriden, CT Marius Damian. Braila, Romania Peter Dowers. Mt. Tom Academy H.S., Holyoke, MA Alenka Slovenia. Rafael Zambrano. Barranquilla, Colombia, SA Brett Grady. Our Lady of Sorrows, Toronto, Ontario, Canada Ginny Turner. Brookstone, Columbus, GA Josh Gow. Sauk Centre HS, Sauk Centre, MN Jessica Marcum. Gloucester City Junior High School Kristin Ammon. Creekwood Middle School, Kingwood, TX Lindsey Landgrover. Creekwood Middle School, Kingwood, TX Ivan Low. Victoria School, Singapore Amanda Tu. Southridge School, Surrey, BC, Canada James Benic. Canada Yee-Lum Mak.  South Pasadena Middle School,  South Pasadena, CA Nikhat Parveen.  University of Georgia, Athens, GA Kelli Uyeda.  South Pasadena High School, South Pasadena, CA Tony Chen. Beck Middle School, Cherry Hill, NJ Catherine Teegler. Forsyth Country Day School, Lewisville, NC Mark Griffin. Westwood College, Dallas, TX

 

 Last Updated On: 4/3/06