# Geocache puzzle help

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

1. 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?

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

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. 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?

:-/

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

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

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

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

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

7. 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.