# Geocaching: Solve a+b=c c/b=b/a Problem

• MHB
• TheCricketer
In summary, the problem discussed is finding the distance between points A and B using proportions. The simplified formulas for this problem include c = a+b, c/b = b/a, (a+b)/b = b/a, a^2 + ab = b^2, (a-b)^2 = ab, and a = (b/2)(√5-1). The solution involves using the Quadratic Formula to find the value of b.
TheCricketer
I love geocaching and a problem that recently came up is:

A--------------B------------C (not to scale)

Find the distance of AB if the proportion of AC:BC is equal to BC:AB. Substituting a for AB, b for BC and c for AC, I come up with:

a+b=c where c/b=b/a

I'm at a loss here. When I put it in WA it comes up with the answer (although looking at the answer, I have no idea how it calculated it) and I was able to "brute force" my answer as well and get the right answer (thanks Excel) but I want to know the math behind it. The actual values are irrelevant as I want to get to the simplified formulas.

Surely, you realize that you can't determine the actual distance from A to B knowing only proportions?

What, exactly, did you put into WA?

You have relationships. Without actual values, that's all you have.

c = a+b -- good

c/b = b/a -- good

You could also write $\dfrac{a+b}{b} = \dfrac{b}{a}$

You could also write $a^{2}+ab = b^{2}$

You could also write $(a-b)^{2} = ab$

You could also write: $a = \dfrac{b}{2}(\sqrt{5}-1)$

Which simplified formulas would you like?

tkhunny said:
You have relationships. Without actual values, that's all you have.

c = a+b -- good

c/b = b/a -- good

You could also write $\dfrac{a+b}{b} = \dfrac{b}{a}$

You could also write $a^{2}+ab = b^{2}$

You could also write $(a-b)^{2} = ab$

You could also write: $a = \dfrac{b}{2}(\sqrt{5}-1)$

Which simplified formulas would you like?

Can you simplify for b please and show the work? I don’t know where the $\sqrt{5}$ comes from.

TheCricketer said:
Can you simplify for b please and show the work? I don’t know where the $\sqrt{5}$ comes from.

This is where you get to demonstrate your love of mathematics. I used the Quadratic Formula with the expression immediately above. There are a few other ways to do it. Show your work!

## 1. What is geocaching?

Geocaching is a real-world outdoor treasure hunting game where participants use GPS-enabled devices to navigate to specific coordinates and find hidden containers called geocaches.

## 2. What is the "solve a+b=c c/b=b/a" problem in geocaching?

The "solve a+b=c c/b=b/a" problem is a common puzzle or challenge found within geocaches. It involves using mathematical equations to solve for the missing variable and uncover the coordinates of the geocache.

## 3. How do I solve the "solve a+b=c c/b=b/a" problem in geocaching?

To solve the "solve a+b=c c/b=b/a" problem, you will need to use basic algebraic principles to solve for the missing variable. This may involve rearranging the equation or using substitution to find the answer.

## 4. Are there other types of puzzles or challenges in geocaching?

Yes, there are many other types of puzzles and challenges in geocaching. Some common ones include decoding ciphers, solving riddles, and completing physical challenges.

## 5. Can I participate in geocaching if I am not good at math?

Absolutely! While some geocaches may involve math puzzles, there are many others that do not require any mathematical skills. Geocaching is a diverse and inclusive activity that can be enjoyed by people of all ages and abilities.

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