{"id":1023,"date":"2017-11-17T22:45:52","date_gmt":"2017-11-17T22:45:52","guid":{"rendered":"http:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/?post_type=chapter&p=1023"},"modified":"2017-12-29T22:13:05","modified_gmt":"2017-12-29T22:13:05","slug":"problem-bank-5","status":"publish","type":"chapter","link":"https:\/\/pressbooks-dev.oer.hawaii.edu\/math111\/chapter\/problem-bank-5\/","title":{"raw":"Problem Bank","rendered":"Problem Bank"},"content":{"raw":"

Problems 34-36 ask you to solve problems about a strange veterinarian who created three mystifying machines.<\/p>\r\n

Cat Machine<\/b>: Place a cat in the input bin of this machine, press the button, and out jump two dogs and a mouse.<\/p>\r\n

Dog Machine<\/b>: This machine\u00a0converts a dog into a cat and a mouse.<\/p>\r\n

Mouse Machine<\/b>: This machine can convert a mouse into a cat and three dogs.<\/p>\r\n

Each machine can also operate in reverse. For example, if you have two dogs and a mouse, you can use the first machine to convert them into a cat.<\/p>\r\n\r\n

\r\n

Problem 34<\/h3>\r\n

The\u00a0veterinarian hands you two cats, and asks you to convert them into exactly three dogs (no extra dogs and no other animals). Can you do it? If yes, say what process you would use.\u00a0 If no, say why not.<\/p>\r\n\r\n<\/div>\r\n \r\n

\r\n

Problem 35<\/h3>\r\n

The\u00a0veterinarian hands you one dog. He says he only wants cats, but he doesn't care how many. Can you help him?\u00a0 How?<\/p>\r\n\r\n<\/div>\r\n \r\n

\r\n

Problem 36<\/h3>\r\n

The\u00a0veterinarian hands you one cat. He says he only wants dogs, but he doesn't care how many. Can you help him?\u00a0 How?<\/p>\r\n\r\n<\/div>\r\n \r\n

Problems 37-40 present several growing patterns made with toothpicks.\u00a0 For each problem you work on, do the following:<\/p>\r\n\r\n

    \r\n \t
  1. Describe in words and pictures how you see the pattern growing.<\/li>\r\n \t
  2. Calculate the number of toothpicks you would need to build the 10th figure in the pattern.\u00a0 Justify your answer based on how the pattern grows.<\/li>\r\n \t
  3. Calculate the number of toothpicks you would need to build the 100th figure in the pattern.<\/li>\r\n \t
  4. Describe how you can figure out the number of toothpicks in any figure in the pattern. Be sure to justify your answer based on how the pattern grows.<\/li>\r\n \t
  5. Could you make one of the figures in the pattern using exactly 25 toothpicks?\u00a0 If yes, which figure? If no, why not? Justify your answer.<\/li>\r\n \t
  6. Could you make one of the figures in the pattern using exactly 100 toothpicks?\u00a0 If yes, which figure? If no, why not? Justify your answer.<\/li>\r\n<\/ol>\r\n \r\n
    \r\n

    Problem 37<\/h3>\r\n

    \"\"<\/p>\r\n\r\n<\/div>\r\n \r\n

    \r\n

    Problem 38<\/h3>\r\n

    \"\"<\/p>\r\n\r\n<\/div>\r\n \r\n

    \r\n

    Problem 39<\/h3>\r\n

    \"\"<\/p>\r\n\r\n<\/div>\r\n \r\n

    \r\n

    Problem 40<\/h3>\r\n

    \"\"<\/p>\r\n\r\n<\/div>\r\n \r\n

    In a mobile<\/i>, the arms must be perfectly balanced for it to hang properly.\u00a0 The artist Alexander Calder was famous for his artistic mobiles.You can view some of his amazing work here<\/a>. Click \u201cExplore Works.\u201d<\/p>\r\n

    Problems 41-42 present you with mobile puzzles. In these puzzles:<\/p>\r\n\r\n