Buttons Case

My first thought was to draw a scale version of the problem on graph paper and see how many patches I could get. I drew a 17 inch by a 22 inch rectangle and cut it into 3 inch by 5 inch sections. I got a 20 pieces when I cut them first vertically. I got 21 pieces when I cut them horizontally. For the third try I did every other row horizontal and vertical but was unable the numbers didn't increase like I thought they would. I asked a few people sitting next to me Chris, Scott, and Ravon about the problem. I realized that maybe if I multiplied 17 by 22 which are 374 and divide it by the patches 3 by 5 which is 15 I may be able to come up with the possible number of possible patches. When I did this I found the number 24.93. This number is a patch of 24 and when I finally tried for the sixth time I came up with this conclusion. When I asked Chris and Scott for help they were very willing to explain. Ravon missed some days but did take the time to explain a little to me as well. Chris was nice enough to show me how to draw the conclusion. I wasn't able to find out the answers to the other patches. I think it was because I focused to much on the first one. I regret not paying full attention in class to my peers, because I would most likely know how to do the other patches as well. The way I did the first answer is most likely how you can figure out the other answers. If you do 17 by 22 which is 374 and divide that by 9 by 10 which is 90 you get 4.156. I came up with the conclusion that if you divide the product of what you get for your piece of satin and how many patches it will give you an idea for the possible answer that you should get. You should then just begin to sketch the answer out and figure out how you can get that many patches.