For my third weekly work I thought I would expand on the Chinese Math handout. I worked on the story problems in that handout and thought I would come up with some of my own word problems that follow similar skills for solution. I will also post solutions to each problem.
1. A Corvette travels at a speed of 80 mph, a Malibu travels at a speed of 75 mph. If the Malibu leaves 1 hour before the Corvette, at what point will the Corvette catch up to the Malibu?
It will take the Corvette 15 hours from it's own start time to catch up with the Malibu. They will meet at 1200 miles.
2. Matt has 15 more stickers than Julie, and 3 more than Megan. Megan has 7 more stickers than Bob and Rachel combined. Rachel and Bob have the same amount of stickers. Rachel has 4 stickers. How many stickers does each person have?
Rachel has 4 stickers
Bob has 4 stickers
Megan has 15 stickers
Matt has 18 stickers
Julie has 3 stickers
3. A large pizza costs $12 and a medium pizza costs $9. A group of friends want to buy 3 large pizzas and 2 medium pizza and each wants to pay their fair share. There are 8 pieces per pizza and no person gets more than 5 slices and no person gets less than 3 slices. No one has change so they all pay to the nearest dollar and have two dollars extra. How many friends are paying for the pizzas? and how much did each friend pay?
There are 8 friends paying for pizza. The price of the pizza comes out to $54. Since there are two dollars extra we know that the friends money totaled $56. There are 40 pieces of pizza total and if no one get more than 5 pieces we know there are at least 8 friends. If no person gets less than 3 slices we know there can't be more than 13 friends. The only number that divides evenly into 56 between 8 and 13 is 8 so there has to be 8 friends paying for the pizza.
4. Let's do some more pizza math because pizza always sounds good to me. If two large pizzas a medium and a small cost $32, 1 large, 3 mediums, and 2 smalls cost $40, and 3 mediums and 2 larges cost $42, then how much does each size pizza cost?
A large pizza will cost about $10.36, a medium pizza will cost about $7.09, and a small pizza will cost about $4.18
This can be solved by using a system of equations such as:
2l+1m+2s=42, 1l+3m+2s=40, 2l+3m=42
I like to use matrices to solve systems of equations.
These are just a few examples of my own "story problems" that follow the same style as those given from the Nine Chapters.
For reference: from Liu Hui's commentary on the Nine Chapters.
ReplyDeleteChapter 6:12. A good runner can go 100 paces while a poor runner covers 60 paces. The poor runner has covered a distance of 100 paces before the good runner sets off in pursuit. How many paces does it take the good runner before he catches up the poor runner.
Chapter 7:1. Certain items are purchased jointly. If each person pays 8 coins, the surplus is 3 coins, and if each person gives 7 coins, the deficiency is 4 coins. Find the number of people and the total cost of the items.
7:18. There are two piles, one containing 9 gold coins and the other 11 silver coins. The two piles of coins weigh the same. One coin is taken from each pile and put into the other. It is now found that the pile of mainly gold coins weighs 13 units less than the pile of mainly silver coins. Find the weight of a silver coin and of a gold coin.
Chapter 8: 1. Top-grade ears of rice, one bundle, medium grade ears of rice, two bundles, low grade ears of rice, one bundle, makes 39 dou. Top-grade ears of rice two bundles, medium grade ears or rice three bundles, low grade ears of rice one bundle makes 34 dou. Top-grade ears if rice one bundle, medium grade ears of rice two bundles, low grade ears of rice three bundles makes 26 dou.
To make an exemplar: consider why these problems, or how did you come up with them, or what is interesting about them. Or generalize about what makes a good problem or how a problem writer can choose numbers that highlight the math involved.