Elementary POW, April 15-19, 1996
Elementary POW Problems || April-June, 1996 Problems || Elementary POW Main Page
****************************************************** Elementary Problem of the Week, April 15-19,1996 This week's problem was submitted by Jody Newman, Center School, Stow MA. Once there lived a farmer, his wife, and their three sons. When the farmer died, his will said that the eldest son was to receive one-half of what he owned, the middle son was to receive one-third, and the youngest son was to receive one-ninth. All the farmer owned, however, was seventeen horses. And try as they might, the three sons could not figure out any way to divide the seventeen horses by their fathers wishes. "Don't worry," their mother told them. "We can solve this with a little help." She went to the neighboring farm and borrowed a horse. Then with a total of eighteen horses, she gave the eldest son one-half, or nine horses. She gave the middle son one-third, or six of the horses. And she gave the youngest son one-ninth, or two of the horses. "There," she said. "Nine plus six plus two makes the seventeen horses your father left you." And she returned the eighteenth horse to the neighbor. How did she do it? ****************************
********************** Amy Forster,age 11, grade 7, home schooling,Cygnet, Australia,email jwilkins@tassie.net.au Wilkins/Forster family Crooked Tree Point.Cygnet. Tasmania.Australia 7112. ph.[002] 951456 ********************** Mike, Nick, Julia, Meghan L., Meghan R. Grade 4 Ms. Seager Bagnall School, Groveland, MA *********************** Brent Durkee, Jon Gunn Grade 6 Mrs. Caruso Bagnall School, Groveland, MA Ian Gugger Grade 6 Mrs. Caruso Bagnall School, Groveland, MA Colin Stokes Grade 6 Mrs. Caruso Bagnall School, Groveland, MA Brian G. and Craig D. Grade 6 Mrs. Caruso Bagnall School, Groveland, MA ************************** Cory, Mike M., Brian Parks Grade 4 Ms. Arria-Lucey Bagnall School, Groveland, MA Alison Morse, Kerry Sniegoski, Heather Quigley Grade 4 Ms. Arria-Lucey Bagnall School, Groveland, MA ************************** Dave Neely - 11 Jason Imbrogno - 11 Burchfield Elementary School Pittsburgh, Pennsylvania Kirstan Gides Krista Ziegler Lindsay Rockot Grade 5b Burchfield Elementary School Pittsburgh, Pennsylvania Stephen Viale grade 5 Burchfield Elementary School Pittsburgh, Pennsylvania ************************* Mrs. Fisher's fourth/fifth grade class Aliso School Carpinteria, California. *************************** Margrethe, Leslie, and Marie Grade 4 Leal School Urbana, IL **************************** Name: Beth Jaxon Grade: 5-6 Teacher's name: Becky and Greg Jaxon School: Learners Unlimited (H.O.U.S.E.) Location: Champaign, IL ***************************** Rebecca, Grade 3 Nancy Kaye Lincoln Elementary Burlingame, CA ***************************** Steve Moleski Mr. Underkoffler's fifth grade class Arrowhead School Methacton School District ***************************** Nicole Petrancosta, Katie Kleppick,Brittany Kress Marzolf 5A Pittsburgh, PA **************************** Dan, Matt, Patrick, Kate, Anthony and Todd Miss Duggan's fourth grade class Munsey Park School Manhasset, NY ***************************** Anita Minakyan, Matt Burke, Ryan Drago and Jeffrey Chin Mrs. Hirn's class Munsey Park School Manhasset, NY ****************************** Ashoke Khanwalkar, grade 3 Western Salisbury School Allentown, PA 18103 ***************************** Kristen Dempsey, Elizabeth Phommathep, John Hale George L. Hess Educational Complex Fifth Grade - Ms. Blair Mays Landing, NJ *******************************
**************************** Amy Forster,age 11, grade 7, home schooling,Cygnet, Australia,email jwilkins@tassie.net.au Wilkins/Forster family Crooked Tree Point.Cygnet. Tasmania.Australia 7112. ph.[002] 951456 17 is a prime number so it can't be divided by anything.You need to find a number divisible by 1/2,1/3, 1/9. ie.divisible by 2,3,and 9. 18=1/2 (of 18) + 1/3(of 18)+ 1/9 (19) = 9+6+2 = 17+1 left over It works because the extra horse from the neighbour makes an even number for dividing in half. Also,by dividing an even number by 2 odd and 1 even number,you get a sum which is odd+even+even =odd,so there is one left over,so you can return the neighbours horse. I explored other numbers divisible by 9,3 and 2 and found this pattern: Let O.N. =Original Number Let N.H. = Neighbours Horse Amount less than O.N.O.N. + N.H.1/2 1/31/9TotalO.N. + N.H. 1718 96217 1 3536 1812434 2 5354 2718651 3 7172 3624868 4 As the original numbers increase, there is an extra horse left over. So for example,if the boys had to share 53 horses and borrowed 1 horse from the neighbour,they would end up giving 3 horses back to their neighbour,so the neighbour would gain 2 horses! I thought this problem was interesting because it was a bit like using a catalyst in chemistry.Is there an area in maths where you change a number(eg make it bigger)so you can solve a problem,then remove it-maybe catalyst numbers?! I tried thinking about such possiblities but did not get very far. ***************************** Mike, Nick, Julia, Meghan L., Meghan R. Grade 4 Ms. Seager Bagnall School, Groveland, MA The mother needed the 18th horse so she had a number she could divide evenly by 2, 3, and 9. If you divide 17 by 2, 3, and 9, you end up with each son getting a fraction of a horse and if you cut a horse up it would be dead. However, if you divide 17 by 2, 3, and 9, the fractions you get are greater than one half so if you round them, you get 9, 6, and 2 as your whole numbers so you really can do the problem without 18 horses. *************************** She needed the eighteenth horse to find the least common multiple of the fractional amounts so that she divide the horses the way the father said. She turned 1/2,1/3, and 1/9 into eighteenths. Then she could solve the problem. Steve Moleski Mr. Underkoffler's fifth grade class Arrowhead School Methacton School District **************************** The farmers wife borrowed a horse making the number of horses 18. One half of 18 is 9, and one third of 18 is 6, and one ninth of 18 is 2. 9+6+2=17, so she can now give back the neighbor's horse. submitted by Mrs. Fisher's fourth/fifth grade class Aliso School, Carpinteria, California. ***************************
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