Challenge 4-6/Ages 9-11
Presented to MathWorld Interactive by Nomads #1 of Pond Creek, Oklahoma
Solutions 1. The facts of the problem that I know are: Breakfast cereal is sold according to how much it weighs. Recycled paper is weighed in an unusual manner. The post office charges based on weight of an item.
2. What I am looking for in the problem is: Is weight a good way to sell cereal? Why is the weight correct but the box is not full? How is weight of recycled paper figured? Why is weight used to figure postal charges? What is a random sample?
3. I thought about the question. I read the cereal box. I used subtraction to figure out how much the recycled paper weighs. That's how I weigh my dog: I get on the scale with her and then without her. If I weigh 70 lbs. with her, and 60 lbs. without her, she weighs 10 lbs. I had to think a lot about why mail is charged by weight because I thought it would make more sense to charge by size. My mom and I talked about it. We know something about weight limits on planes, because my dad is a pilot. My mom and I talked a lot about random samples and average weights.
4. Here are my solutions:I don't think I have been cheated because the cereal isn't to the top of the box. They fill it up to the top, but when it's being shipped, the truck bounces and the bounces make it pack down. The box says that it settles during shipment. I think weight is a good way to sell cereal because it is consistent between all the boxes. I can't think of a better way to sell cereal.
To calculate the weight of the paper, subtract the weight of the truck without the paper from the weight of the truck with the paper. For example, if the truck weighs 5000 lbs. with the paper and 4000 lbs. without the paper, the paper weighs 1000 lbs. 5000 lbs. - 4000 lbs. = 1000 lbs.
Weight is used instead of size for postal charges maybe because if it's being sent by plane, then they would have to weigh it because planes have weight limits.
A random sample is when the clerk just grabs some mail instead of "choosing" it for some reason like an outrageous orange envelope or because it's big.
To find the weight of one piece of mail, the clerk divides the total weight of the sample by the number of items.
If the clerk weighed just one, it would only give a single weight. Some may weigh 1 1/2 oz., others 3/4 oz. If the clerk got one measurement that was way low or high, they would be off on the average weight.
5. I checked my work be reading over my solutions to see if they made sense.
6. Ask your parents to save their junk mail for a week. With a postal scale, weigh each piece. Then take a random sample and weigh them and take an average. See how close they are. Look at the postmark to see how much it cost to mail each piece.