







Working backwards 
20200605 

Jill pose la question : Emma has a bunch of grapes (1)/(2 ) of it she gave it to her friend and (3)/(4 ) of the remaining grapes she gave it to Gina. There are 4 grapes remaining. So how many bunch of grapes to begin with? Harley Weston lui répond. 





Working backwards 
20150827 

Heather pose la question : Tom took a collection of tiles from a box. Sue took 13 and Bob
took half of those remaining. Tom had 11 left. How many did they start with? Penny Nom lui répond. 





How many boats total are in the marina? 
20150415 

Carla pose la question : In a marina, 3/4 of the boats are white, of the remainder 4/7 are blue, the rest are red. There are 9 red boats. How many boats total are in the marina? My answer is 84 because if 1/4 of the boats are divided into sevenths, that makes the whole marina a 28 part item. 3/28 are red so 84 is the total number of boats. My child thinks I am wrong. Penny Nom lui répond. 





Mary gave her sister 5/8 of her nuts 
20150122 

Valence pose la question : Mary gave her sister 5/8 of her nuts. Her sister gave her friend 2/3 of the amount, and her cousin 1/3 of the remainder. If Mary's sister had 50 nuts left, how many nuts had Mary. Penny Nom lui répond. 





Grandpa had an apple tree 
20140914 

Emma pose la question : Grandpa had an apple tree. On the first day half of the apples plus one fell to the ground. On the second day, half of the remaining apples plus one fell to the ground. On the third day, half of what was left plus one fell to the ground. The tree was left with only one apple now. How many apples did the tree produce originally? Penny Nom lui répond. 





Brandon went shopping  working backwards 
20140711 

Sindy pose la question : Brandon went shopping & spent 1/4 of his money on shoes & 1/5 of the remainder on a new wallet. He then spent $60 on a pair of jeans. If he had $60 left, how much did Brandon start with? Penny Nom lui répond. 





Working backwards 
20130728 

Petal pose la question : Tom bought some oranges. He threw 37 rotten oranges and bought 56 more. Finally he had 220 oranges. How many oranges did Tom had at first? Penny Nom lui répond. 





How many oranges? 
20121006 

Rodger pose la question :
Question from Rodger, a teacher:
How Many Oranges?
Marjorie, Colleen, and Bob picked oranges together. They were tired after picking a large number of oranges and so fell asleep. Marjorie woke first and decided to take her third of the oranges and head home. She counted the oranges, and found that the number was divisible by 3 if she took one of the oranges first. Marjorie took one orange and then took onethird of the remaining oranges. She left quietly.
Bob awoke a short time later, noticed that Colleen was sleeping, and presumed Marjorie had gone for a walk. He decided to head home because he wasn't feeling well. Not realizing that anyone had left, he counted the oranges and found that the number of oranges was two more than a number that could be easily divided by 3. So he took the two extra oranges and then onethird of what was left. He left without waking Colleen and without waiting for Marjorie to return.
Colleen finally awoke and wondered where her friends had gone. She assumed they were both busy somewhere nearby. Before she left, she counted the oranges and was surprised at how small the number was. She found that the number of oranges was one more than a multiple of three, so she took the extra orange and one third of those remaining.
1. What was the total number of oranges the friends picked?
2. How many oranges were left behind when Colleen departed?
3. Is more than one answer possible for the total number of oranges? If so, what other numbers are possible? Explain.
4. Based on the values you found in problem 3, determine a reasonable solution to the problem. Explain your answer.
5. Is it possible that five oranges remained after Colleen took her share? Explain.
6. Could there have been six oranges left after Colleen departed? What about 46 oranges initially? Explain
7. Find a pattern that gives all the possible numbers of oranges that the friends picked. Explain your pattern
5. Is it possible that five oranges remained after Colleen took her “share”? Explain.
6. Could there have been six oranges left after Colleen departed? What about 46 oranges initially? Explain
7. Find a pattern that gives all the possible numbers of oranges that the friends picked. Explain your pattern Penny Nom lui répond. 





Problem solving 
20111027 

keelan pose la question : a number is divided by 5. then 3 is added to the quotient. after subtracting 10, the results is 30.what is the number.t Penny Nom lui répond. 





Working backwards 
20110310 

Kevin pose la question : Duwayne wrote a two digit number.He multiplied it by 3,added 18, and divided by 8.His final answer was 9.What number did Duwayne write Penny Nom lui répond. 





Working backwards 
20100622 

Martha pose la question : Karen spent all but $8.00 of her savings in three stores. In each store
she spent $2.00 less than half of what she had when she went in. How
much money did Karen have at the start. Robert Dawson lui répond. 





Working backwards 
20100411 

adel pose la question : alice gave reggie and freddie as much money as each had already.reggie in turn gave alice and friddie as much money as each already had in negotiable treasury notes. freddie gave alice and reggie as much money as they each had. in the end they each had the same sum, 24000.00.how much money did they each in the beginning? Penny Nom lui répond. 





An afternoon at the races 
20090515 

garths pose la question : A professional gambler was betting at a horse racing afternoon.
At the end of the first race he had doubled his money.
He bet R30 on the second race and tripled the money he came with.
He bet 54 on the third race and quadrupled (4 times) the money he came with.
He bet R72 on the fourth race and lost it all. But he still had R48 left.
How much money did he take to the race track? Harley Weston lui répond. 





Marcia's summer earnings 
20090311 

Yasmine pose la question : Marcia saved money by working over the summer. Before school started, she spent 25%of the money of jewelry
and then 2/3 of the remaining money on a digital camera. She still had $213 left. How much money did she have
before she started shopping? Robert Dawson and Penny Nom lui répond. 





A bag of coins 
20090109 

marina pose la question : I have a bag of gold coins. I give 1/8 to mother then gave 1/2 of what was left to my brother
i give 2/7 of what was left to father. If i have 25 coins left. how many do i have originally. Robert Dawson and Penny Nom lui répond. 





A game for 5 players 
20081116 

safdar pose la question : five players agreed that after every game, the loser doubles every body's money. they played 5 games and everybody lost once. after the 5 games, everybody had 4128. How much money did each of the players have before the game? show your work. Janice Cotcher and Harley Weston lui répond. 





Fibonacci numbers 
20080130 

Beth pose la question : You've answered a question for a Linda Bach on Oct. 25, 1999 that has to do with a pet rabbit and stairs. (Working Backwards) We were wandering if there is a formula we can use to plug the numbers in? My 7th grader got that exact same problem. I've spent several hrs trying to come up with a formula. I've tried the combinations formula, the Pascal's triangle and the Permutations formula. It seems like it is something real close to those, but can't quite get anything to work. What kind of formula would work for finding the outcome of this problem? Thanks so much for your help. Beth Penny Nom lui répond. 





Ridingcap's daughter 
20061023 

Marcus pose la question : Ridingcap's daughter,whose real name was Coleen, set out for grandma's house again. This time she was delivering jam and jellies. First she stopped to see Mrs. Parsley,who took in grandma's mail while grandma was @ the hospital recovering from the wolf. Colleen gave Mrs. Parsley one third of the jars in her basket. Then Colleen set out again,and suddenly the wolf jumped out behind the bush and grubbed one half of the jars in Colleen's basket. When the wolf ran off, Colleen went on and gave Mr .Woodsman two thirds of what was left in her basket. Colleen had six jars of jam and jellies left for grandma. HOW MANY JARS DID COLLEEN LEAVE HOME WITH Stephen La Rocque lui répond. 





A bicycle ride around the local lakes 
20060511 

Geecee pose la question : Yesterday I went for a long bicycle ride around the local lakes. As the ride was quite long, I rode in various stages. In the first stage I rode half of the overall distance. Stage two saw half of the remaining distance plus 35 metres covered. Stage three covered threequarters of the remaining distance. Stage four completed half of the remaining distance plus 75 metres. Stage five completed the journey with a final burst of 150 metres.
How far did I cycle in total? Stephen La Rocque lui répond. 





How many passengers boarded the plane in Phoenix? 
20051103 

Vish pose la question : Passengers boarded a plane in Phoenix. In Dallas 1/2 of the passengers got off and 4/5 of the original number got on. In Memphis 3/4 of the passengers got off and twice the number of remaining passengers got on. In Chicago 2/3 of the passengers got off the plane leaving 39 passengers. How many passengers originally boarded the plane in Phoenix? Penny Nom lui répond. 





What number am I? 
20051027 

Samantha pose la question : First 8 is added to me, then I am multiplied by 6. Then 40 is subtracted from me. Finally, I am divided by 10. The result is 11. What number am I? Penny Nom lui répond. 





Red riding hood 
20040214 

Frank pose la question : Red riding hood had a number of jars to take to grandma's house. As she traveled she gave away 1/3 of them to an old lady. Then later As she walked through the forest a wolf stole 1/2 of her remaining jars. When she arrived at grandma's house she gave her 2/3 of the remaining jars. She kept 6 jars for herself. How many jars did she start out with. Diane Hanson lui répond. 





Working backwards 
20030314 

Melody pose la question : Triva went to the ardcade at the state fair to win some goldfish. She already had some goldfish at home, but wanted more. She won enough goldfish to double her stock. Her mom made her give four away. She put her new ones in the tank with the others, by the morning half of the goldfish had died. Triva's friend gave her six more. The next morning twothirds of her goldfish died. She was left with two goldfish after giving one to a friend. How many goldfish did she start with? Penny Nom lui répond. 





Dorothy and the wizard 
20030124 

Ken pose la question :
dorothy was going to see the wizard of oz...she stopped at the bakery and bought a box of cookies. she met the scarecrow and gave him half the cookies. she ate half of the remaining cookies and threw one half cookie away. she met the tin man and gave him half the cookies. she ate half the remaining cookies and threw one half cookie away. she met the lion. she gave him half of her cookies. she ate half the remaining cookies and threw the LAST half cookie away. how many cookies did dorothy leave the bakery with? Penny Nom lui répond. 





Tonya in the orange grove 
20010425 

A parent pose la question : Tonya was helping in the orange grove. She decided to take some oranges home to share with 3 friends. She gave 3 more than half to Jennifer. Angela got half the remainder and 3 more. She gave Josie half the remainder plus three. When she got home, she had only 10 oranges left. How many did she have when she left the grove? Penny Nom lui répond. 





A bargin with the devil 
20010321 

DJ pose la question : There once was a boy who spent all his time dreaming about getting rich. " I would do anything to be rich". The devil, hearing this, appeared before the boy and offered to make him rich. "See that bridge?" said the devil. Just walk across and I will double your money you have now. In fact, each time you cross I will double your money. There is just one thing you must give me $24 after each crossing. The boy agreed. He crossed the bridge, stopped to count his money and, and sure enough, it had doubled. He paid the devil $24 and crossed again. Again his money doubled. He paid another $24 and crossed a third time. Again his money had doubled, but this time there was only $24 left which he had to pay the devil so he was left with nothing. The devil laughed and vanished.  How much money did the boy start with?
Penny Nom lui répond. 





A merchant from Pisa 
20010211 

A student pose la question : A merchand doing business is Lucca doubled his money there and spent 12 denarii. On leaving, he went to Florence, where he also doubled his mone and spent 12 denarii. Returning home to Pisa, he there doubled his money and again spent 12 denarii, nothing remaining. How much did he have in the beginning? Claude Tardif lui répond. 





Working Backwards 
19991016 

Linda pose la question : I am having problems finding examples of problems that require "Working Backwards" used as a strategy for solving. We are required to give a presentation on Monday, October 25, 1999 in our school districts math class. We are trying to become better problem solvers and how to teach problem solving in the elementary classroom. Help! I can't find anything in my web searches. Penny Nom lui répond. 

