Halloween is celebrated in many western countries. It comes on October 31, as the eve of the Christian feast of All Hallows’ Day. Unlike the remembrance day which recognizes the death of only one’s own warriors, Halloween is to remember all dead including saints (hallows), martyrs, and all the faithful departed. There are several theories on its origin and the traditions associated with it. Today the main activities of Halloween include trick-or-treating, Halloween costume parties, carving pumpkins into jack-o’-lanterns, bonfires, apple bobbing, divination games, pranks, visiting haunted attractions, telling scary stories, and watching horror movies. Today none of these activities are associated with a religion but they are accepted as social activities in the West. Children wait for this day because they can go trick or treating. Trick or treating has become a social event. Children go door to door in their neighbourhood and say “Trick or Treat”. The host greets the kids at the door and gives them a treat – mostly a candy, some salty snack and occasionally money. People do not give apples anymore because a few year ago some sickos put blades in them. If kids are small, parents accompany them. This gives them a chance to say an annual hello to the neighbours.
The kids take the loot home. Their parents inspect what they received. then the kids often negotiate with their parents what they can eat that day and the next day etcetra.
David has been trick or treating for many years now. He thinks that he is old enough to go on his own so that he can go to many more places. Despite all of his whining, his mother Iona does not think that he is ready to go alone yet.
Being a responsible mother, Iona focuses on David’s education. She also wants him to learn about money. So she took David with her for Halloween shopping. David had decided to dress up as a rock star. So he picked up a rock star costume, and his mother bought it for him. They also picked up two giant boxes of candy. One was a 100 pack of mix of different chocolates that cost them $18, and the second was a brand name mix of chocolates which cost $22 for a pack of 50. All these were small chocolates.
David: How many kids is this candy for ?
Iona: I think 50 kids should show up. So we will give each of them three candies – two from the first box and one from the second.
David: Mom, 18 plus 22 is $40. We are spending $40 on candy for 50 kids. Because $40 is 4000 cents and 4000 divided by 50 is 80, it comes to 80 cents per kid.
Iona: Do you think it is too much ?
David: I don’t know. I will tell you after I find out what I get from everyone.
Jim, the neighbor’s kid and David went trick or treating with their moms while their fathers stayed at home to greet the kids coming to their homes. The evening was getting cooler especially with a howling wind which was typical for Halloween day in this part of the country. David had a big pillow case and Jim had brought a large grocery bag. Each house they went to, Jim and David would say trick or treat and people would put something in their bags. Then, they would say thank you and quickly move onto the next house. They did not want to waste any time because they wanted to go to as many houses as possible. Their mothers would either talk to the hosts (barely) or to each other. They just went around two blocks which was more than most kids their age. That was 60 houses that they went to.
David came home, opened his bag, poured all the loot on the big dining table, and said: Look at it. I got all this. There are many types of treats – $3 in money, 10 bags of potato chips, 10 chocolate bars like the ones we got for $22 for 50 bars, 30 looks like the bars we paid $18 for 100 bars, and some cheap candy.
Iona: We saw these potato chips bags which were 20 bags to a pack. They were $8 for a pack. I guess your cheap candy must be worth two dollars also.
David was curious about the price of his loot. So he started writing.
| Coins | $3.00 | |||
| Potato chips | 10 | $8 per 20 bags | 10 x 8 /20 = $4.00 | $4.00 |
| Expensive chocolates | 10 | $22 per 50 bars | 10 x 22 /50 = $4.40 | $4.40 |
| Other chocolate bars | 30 | $18 per 100 | 18 x 30/100 = $5.40 | $5.40 |
| Other candy | $3.00 | |||
| Total loot | $19.80 |
David brought his calculator. He calculated that he had received a total of $19.80 worth of stuff from 60 houses. So he calculated that 1980 cents divided by 60 was 33. That meant that on average each house had given him 33 cents worth of material.
David: Mom, I only got 33 cents worth of stuff per house. We spent 80 cents per kid. That was way more than others spent.
Iona: Some houses gave you coins and other gave you candies. What did you like better ?
David: Of course, money mom. Then I can buy anything I want.
Iona: David, it’s good that you went to 60 houses. You met many people in the neighbourhood. I am sure you made new friends. That may be more important than just collecting the stuff.
David (as if he ignored this message): Mom. Next year we should give everybody two quarters. That way you will spend less money and the kids will be happy.
Challenge
David had a calculator to divide 19.80 by 60. How would you go about without it ?
Solution: One boring method will be to do the long division. Another way would be to think:
$19.80 is 1980 cents, 1980 divide by 60 is the same as 198 divided by 6.
198 is the sum of 180 and 18.
Because 3 x 6 is 18 and 30 times 6 is 180, 198 divided by 6 must be 30 + 3 or 33.
Supplementary
Jim and Sophie are brother and sister of similar age. Jim is 9 years of and Sophie is 8. They are always competing. They both went trick and treating around their block for an hour.
Mom: Put all your candy out in the open. I want to inspect each piece before you eat anything.
So Jim placed all his candy on one end of the dining table and Sophie did so on the other. While mom was inspecting the candy, the kids started to argue.
Sophie: I think I got more stuff than you do.
Jim: How so ? How are we going to compare ?
Sophie: We have 50 g chocolates, 20 g chocolates. sugar candy and some money.
Jim: Ok, we will say 50 g chocolate is worth 100 cents, 20 worth 40 cents, wrapped sugar candy worth 10 cents and the cash is what it is. I got 8 of the 50 g chocolates worth 800 cents, 25 smaller chocolates worth 25 x 40 or 1000, 25 wrapped candy worth 25 x 10 = 250 cent, and 150 cents in cash.
| Jim | Sophie | ||
| 50 g chocolate (100 cents each) | 8 x 100 = 800 | 14 x 100 = 1400 | |
| 20 g chocolate (40 cents each) | 25 x 40 = 1000 | 20 x 40 = 800 | |
| Sugar candy (10 cents each) | 25 x 10 = 250 | 0 x 100 = 0 | |
| Cash | 150 | 200 | |
| Total value | 2200 | 2400 | |
Sophie: So your stuff is worth 800 + 1000 + 250 + 150 = 2200 cents or $22.
Jim: You have 14 of the 50 g chocolates which is 1400 cents, 20 smaller chocolates worth 20 x 40 or 800 cents, no sugar candy and 200 cents in cash.
Sophie: So that is 1400 + 800 + 200 = 2400 cents or $24. So I got more than you.
Jim: I guess, I got more in number and you got better value.
Math Stories For You 