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  • 1. Solution to Problem of the Week!
    • Let X be the original amount of coconuts
    • 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. Use the same equation for the remaining monkeys
    • 4. So the equation set would be
    • 5. b = (6/7)*(x-1) = amount after 1 monkey,
    • 6. c = (6/7)*(b-1) = amount after 2 monkeys,
    • 7. d = (6/7)*(c-1) = amount after 3 monkeys,
    • 8. e = (6/7)*(d-1) = amount after 4 monkeys,
    • 9. f = (6/7)*(e-1) = amount after 5 monkeys,
    • 10. g = (6/7)*(f-1) = amount after 6 monkeys,
    • 11. h = (6/7)*(g-1) = amount after 7 monkeys,
    • 12. i = (1/7)*(h-1) = amount each got at the end.
    • 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
  • 14.
    • Now the equations from the last slide need to be simplified
    • 15. b = (6/7)*(x-1) Multiply each side by 7
    • 16. 7B=6*(x-1) Distribute out the 6
    • 17. 7B=6x-6 Put the six on one side of the equation and the variables on the other
    • 18. 6=7B+6x
    • 19. Repeat this process with the remaining equations; you get
    • 20. 6a - 7b = 6,
    • 21. 6b - 7c = 6,
    • 22. 6c - 7d = 6,
    • 23. 6d - 7e = 6,
    • 24. 6e - 7f = 6,
    • 25. 6f - 7g = 6,
    • 26. 6g - 7h = 6,
    • 27. h - 7i = 1
  • 28.
    • As you eliminate all the variables except X and I you will get
    • 29. 6^1x - 7^1b = 6*(7^1 - 6^1)
    • 30. 6^2x - 7^2c = 6*(7^2 - 6^2)
    • 31. 6^3x - 7^3d = 6*(7^3 - 6^3)
    • 32. 6^4x - 7^4e = 6*(7^4 - 6^4)
    • 33. 6^5x - 7^5f = 6*(7^5 - 6^5)
    • 34. 6^6x - 7^6g = 6*(7^6 - 6^6)
    • 35. 6^7x - 7^7h = 6*(7^7 - 6^7)
    • 36. 6^7x - 7^8i = 7^8 – 6^8
    • 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. 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)
  • 39.
  • 49. Solution
    • 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.