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Solution to Problem of the Week! <ul><li>Let X be the original amount of coconuts
The amount of coconuts after on monkey has finished will equal b = (6/7)*(x-1) where b is the number of coconuts.
Use the same equation for the remaining monkeys </li></ul>
<ul><li>So the equation set would be
b = (6/7)*(x-1) = amount after 1 monkey,
c = (6/7)*(b-1) = amount after 2 monkeys,
d = (6/7)*(c-1) = amount after 3 monkeys,
e = (6/7)*(d-1) = amount after 4 monkeys,
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Fgrsdg

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Transcript of "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 </li></ul>
  4. 4. <ul><li>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 </li></ul>
  37. 37. <ul><li>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. Solution <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 </li></ul>
  44. 44. <ul><li>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>
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