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# Fgrsdg

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### Fgrsdg

1. 1. Solution to Problem of the Week! <ul><li>Let X be the original amount of coconuts
2. 2. The amount of coconuts after on monkey has finished will equal b = (6/7)*(x-1) where b is the number of coconuts.
3. 3. Use the same equation for the remaining monkeys
4. 4. So the equation set would be
5. 5. b = (6/7)*(x-1) = amount after 1 monkey,
6. 6. c = (6/7)*(b-1) = amount after 2 monkeys,
7. 7. d = (6/7)*(c-1) = amount after 3 monkeys,
8. 8. e = (6/7)*(d-1) = amount after 4 monkeys,
9. 9. f = (6/7)*(e-1) = amount after 5 monkeys,
10. 10. g = (6/7)*(f-1) = amount after 6 monkeys,
11. 11. h = (6/7)*(g-1) = amount after 7 monkeys,
12. 12. i = (1/7)*(h-1) = amount each got at the end.
13. 13. This works as the original number of coconuts must be able to be subtracted from 6/7 when one is subtracted from the original number and form an integer </li></ul>
14. 14. <ul><li>Now the equations from the last slide need to be simplified
15. 15. b = (6/7)*(x-1) Multiply each side by 7
16. 16. 7B=6*(x-1) Distribute out the 6
17. 17. 7B=6x-6 Put the six on one side of the equation and the variables on the other
18. 18. 6=7B+6x
19. 19. Repeat this process with the remaining equations; you get
20. 20. 6a - 7b = 6,
21. 21. 6b - 7c = 6,
22. 22. 6c - 7d = 6,
23. 23. 6d - 7e = 6,
24. 24. 6e - 7f = 6,
25. 25. 6f - 7g = 6,
26. 26. 6g - 7h = 6,
27. 27. h - 7i = 1 </li></ul>
28. 28. <ul><li>As you eliminate all the variables except X and I you will get
29. 29. 6^1x - 7^1b = 6*(7^1 - 6^1)
30. 30. 6^2x - 7^2c = 6*(7^2 - 6^2)
31. 31. 6^3x - 7^3d = 6*(7^3 - 6^3)
32. 32. 6^4x - 7^4e = 6*(7^4 - 6^4)
33. 33. 6^5x - 7^5f = 6*(7^5 - 6^5)
34. 34. 6^6x - 7^6g = 6*(7^6 - 6^6)
35. 35. 6^7x - 7^7h = 6*(7^7 - 6^7)
36. 36. 6^7x - 7^8i = 7^8 – 6^8
37. 37. In the last problem X: Is going to be -6(match the 6^7X on the left side to the -6^8 on the right. You need a negative and one more six to make the two terms equal)
38. 38. In the last problem;I is going to equal -1(again match the -7^8i on the left to the 7^8 on the right) </li></ul>
39. 39. <ul><li>So to find the solution
40. 40. X=-6 + 7^8*T
41. 41. And
42. 42. I=-1 + 6^7*T
43. 43. T is any integer
44. 44. Set T equal to one, as that is the lowest positive integer
45. 45. X=-6+7^8(1)
46. 46. X=5,764,795
47. 47. I=-1+6^7(1)
48. 48. I=279,935 </li></ul>
49. 49. Solution <ul><li>So there was at least 5,764,795 coconuts to start with and in the end, and each monkeys received at least 279,935 coconuts in the morning. </li></ul>