# Thread: Problem Solving with bases

1. ## Problem Solving with bases

I wasn't sure which heading to put this under since it is for Problem Solving for Elementary Teachers...here is the problem.

In Alphabetville symbols symbols for numbers do not exist as we know them. In fact all numbers are represented by letters of the alphabet. Each letter A through Z represents consecutively a number starting with A being zero. What base are the people of Alphabetville using?

Using the numeration system of Alphabetville, solve the following problem:

TWO + TWO
(be sure the answer is written in letters)

I understand how to change numbers from base to base,etc. ButI get really confused with letters. Any suggestions or hints will be greatly appreciated. Thank you.

2. Originally Posted by ambergarrett955
I wasn't sure which heading to put this under since it is for Problem Solving for Elementary Teachers...here is the problem.

In Alphabetville symbols symbols for numbers do not exist as we know them. In fact all numbers are represented by letters of the alphabet. Each letter A through Z represents consecutively a number starting with A being zero. What base are the people of Alphabetville using?

Using the numeration system of Alphabetville, solve the following problem:

TWO + TWO
(be sure the answer is written in letters)

I understand how to change numbers from base to base,etc. ButI get really confused with letters. Any suggestions or hints will be greatly appreciated. Thank you.
Let me see if I am understanding the problem.

A=0 and Z=9

A,B,C,....Z =26 numbers. So we want to split the interval [0,9] on the number line into 26 equally spaced intervals? So that $\displaystyle B=\frac{9}{26}$ and $\displaystyle C=B+B$ right?

3. Yes, A-Z is 0-9.

4. Originally Posted by ambergarrett955
Yes, A-Z is 0-9.
Ok, so in this number system, the WORD "TWO" wouldn't refer to the NUMBER 2, it would would refer to "C". So we want to find TWO plus TWO i.e. C+C right?

Ok, so $\displaystyle B=\frac{9}{26}$, $\displaystyle C=B+B=\frac{18}{26}$

So $\displaystyle C+C=\frac{18+18}{26}=\frac{36}{26}=\frac{18}{13}$.

I think this should be right so far. So now we want to right this in terms of the letters right?

5. lol, now I'm with you. I'm confused too. I want to just say the answer is D.

Edit, the answer is "E" I think.

6. Thank you for you help. I just find that this is so confusing. lol I appreciate it!