Geocache puzzle help

Discussion in 'Calculator Requests' started by Lacey, Dec 26, 2016.

  1. Lacey

    Lacey New Member

    In the first hour, he sold one-half of his sticks, plus one-half of a stick. The next hour, he sold one-third of his remaining sticks plus one-third of a stick. In the third hour, he sold one-fourth of what he had left, plus three-fourths of a stick. The last hour, he sold one-fifth of the remaining sticks, plus one-fifth of a stick. He did not cut up any sticks to make these sales. He returned home with 19 sticks. How many did he originally take to the event?


  2. math_celebrity

    math_celebrity Administrator Staff Member

    Let x equal the number of sticks he started with. We have:
    The equation is 4/5 * (3/4 * (2/3 * (0.5x - 0.5) -1/3) - 0.75) - 0.2 = 19

    Add 0.2 to each side:
    4/5 * (3/4 * (2/3 * (0.5x - 0.5) -1/3) - 0.75) = 19.2

    Multiply each side by 5/4
    (3/4 * (2/3 * (0.5x - 0.5) - 1/3) - 0.75) = 24

    Multiply the inside piece first:
    2/6x - 2/6 - 1/3
    2/6x - 4/6

    Now subtract 0.75 which is 3/4
    2/6x - 4/6 - 3/4

    4/6 is 8/12 and 3/4 is 9/12, so we have:
    2/6x - 17/12

    Now multiply by 3/4
    6/24x - 51/48 = 24

    Simplify:
    1/4x - 17/16 = 24

    Multiply through by 4
    x - 17/4 = 96

    Since 17/4 = 4.25, add 4.25 to each side
    x = 100.25

    Since he did not cut up any sticks, he has a full stick to start with:
    So x = 101
    Lacey likes this.


  3. Lacey

    Lacey New Member

    Ok. To go further in this equation. It reads:
    ...How many did he originally take to the event? Multiply the answer by 3 and reverse the digits. This will give you the answer for ACH in the coordinates.

    Does that make sense to reverse 303?

    :-/

    Thank you for your help!!


  4. math_celebrity

    math_celebrity Administrator Staff Member

    Let x equal the number of sticks he started with. We have:
    The equation is 4/5 * (3/4 * (2/3 * (0.5x - 0.5) -1/3) - 0.75) - 0.2 = 19

    Add 0.2 to each side:
    4/5 * (3/4 * (2/3 * (0.5x - 0.5) -1/3) - 0.75) = 19.2

    Multiply each side by 5/4
    (3/4 * (2/3 * (0.5x - 0.5) - 1/3) - 0.75) = 24

    Multiply the inside piece first:
    2/6x - 2/6 - 1/3
    2/6x - 4/6

    Now subtract 0.75 which is 3/4
    2/6x - 4/6 - 3/4

    4/6 is 8/12 and 3/4 is 9/12, so we have:
    2/6x - 17/12

    Now multiply by 3/4
    6/24x - 51/48 = 24

    Simplify:
    1/4x - 17/16 = 24

    Multiply through by 4
    x - 17/4 = 96

    Since 17/4 = 4.25, add 4.25 to each side
    x = 100.25

    Since he did not cut up any sticks, he has a full stick to start with:
    So x = 101


  5. math_celebrity

    math_celebrity Administrator Staff Member

    Let x equal the number of sticks he started with. We have:
    The equation is 4/5 * (3/4 * (2/3 * (0.5x - 0.5) -1/3) - 0.75) - 0.2 = 19

    Add 0.2 to each side:
    4/5 * (3/4 * (2/3 * (0.5x - 0.5) -1/3) - 0.75) = 19.2

    Multiply each side by 5/4
    (3/4 * (2/3 * (0.5x - 0.5) - 1/3) - 0.75) = 24

    Multiply the inside piece first:
    2/6x - 2/6 - 1/3
    2/6x - 4/6

    Now subtract 0.75 which is 3/4
    2/6x - 4/6 - 3/4

    4/6 is 8/12 and 3/4 is 9/12, so we have:
    2/6x - 17/12

    Now multiply by 3/4
    6/24x - 51/48 = 24

    Simplify:
    1/4x - 17/16 = 24

    Multiply through by 4
    x - 17/4 = 96

    Since 17/4 = 4.25, add 4.25 to each side
    x = 100.25

    Since he did not cut up any sticks, he has a full stick to start with:
    So x = 101


  6. math_celebrity

    math_celebrity Administrator Staff Member

    No, he started with 101, and that is how he got down to 19.


  7. Lacey

    Lacey New Member

    Let me post the whole equation paragraph:

    Brainteaser # 1: Answer for ACH

    A fellow geocacher decided that he would try to sell some hand-made walking sticks at the local geocaching picnic event. In the first hour, he sold one-half of his sticks, plus one-half of a stick. The next hour, he sold one-third of his remaining sticks plus one-third of a stick. In the third hour, he sold one-fourth of what he had left, plus three-fourths of a stick. The last hour, he sold one-fifth of the remaining sticks, plus one-fifth of a stick. He did not cut up any sticks to make these sales. He returned home with 19 sticks. How many did he originally take to the event? Multiply the answer by 3 and reverse the digits. This will give you the answer for ACH in the coordinates. Make sure to multiply and reverse the digits.

    What would the answer be?


  8. math_celebrity

    math_celebrity Administrator Staff Member

    Multiply the answer by 3: 101 * 3 = 303

    Reverse the digits:
    303 reversed is a palindrome, so it's still 303.


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