# Homework Help: Number system?

1. Dec 6, 2009

### mmekosh

1. The problem statement, all variables and given/known data
What is the base of the system in which 121 represents the same number as the decimal number 324?

2. Relevant equations

3. The attempt at a solution
Can you please just explain to me what this means? I don't think we've learned it, and all the explanations I have found online are no help. I have no clue what the question is asking, but if someone could please reword perhaps what the question is asking, I'm sure I could figure it out. Thanks so much!
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Dec 6, 2009

### jegues

We count using base 10. The decimal number 324 can be defined as follows:

3*(10^2) + 2*(10^1) + 4(10^0) = 324.

So,

324 = 1*(X^2) + 2*(X^1) + 1*(X^0)

This is now a quadratic equation which you can solve. The CORRECT resulting zero will be the base of the system in which the number 121 corresponds to 324 in base 10.

3. Dec 6, 2009

### Staff: Mentor

The digits in a number in the decimal (base-10) system represent increasingly higher powers of 10. The decimal number in this problem, 324, represents 3*102 + 2*101 + 4*100, or 300 + 20 + 4.

What this problem is asking for is the base b for which 1*b2 + 2*b + 1 is the same number as 324. One way to do this problem is trial and error - take a guess at what b might be, and see what 121b equal as a base-10 number.

Hint: Try values for b that are larger than 10.

4. Dec 6, 2009

### mmekosh

Ok, thank you so much! This helped a lot.