Solving the Frustrated Band Director Problem!

Understanding the Problem

Read the problem over and make sure you understand it. Pick out important information. The data I felt was important is in bold letters.

The frustrated band director had his people march by two's, but there was one person left over. So he had them march by three's, but then there were two people extra. When he had them march by four's, there were three left over, and when he had them march by five's, there were four left over. How many people were there in his band?

Devising a Plan

The method I decided to use in this problem is trial and error. I decided I should take five and multiply it by another number and then add four. After this I am going to try this number with the other numbers to see if it will meet all the conditions. I decided to start with three and work my way up.

Carrying Out the Plan and Looking Back

5 * 3 + 4 = 19

19 / 4 = 4 with 3 left over, 19 / 3 = 6 with one left over, doesn't work

5 * 4 + 4 = 24

24 / 4 = 6 none left, this number isn't right

5 * 5 + 4 = 29

29 / 4 = 7 with one left, try again

5 * 6 + 4 = 34

34 / 4 = 8 with two left, no good

5 * 7 + 4 = 39

39 / 4 = 9 with three left, 39 / 3 = 13

5 * 8 + 4 = 44

44 / 4 = 11

5 * 9 + 4 = 49

49 / 4 = 12 with one left

5 * 10 + 4 = 54

54 / 4 = 13 with two left

5 * 11 + 4 = 59

59 / 4 = 14 with 3 left over, 59 / 3 = 19 with two left, 59 / 2 = 29 with one left, this is the answer!

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S. A. Hudson: SHUDSON@nmu.edu.