In a number system the product of 44 and 11 is 1034. The number 3111 of this system, when converted to the decimal number system, becomes

To solve this problem, we first need to determine the base \( b \) of the number system. Given that the product of \( 44_b \) and \( 11_b \) equals \( 1034_b \), we'll start by converting the numbers from base \( b \) to decimal (base 10).

### Step 1: Convert the numbers from base \( b \) to decimal
1. **Convert \( 44_b \) to decimal**:
   \[
   44_b = 4b + 4
   \]
2. **Convert \( 11_b \) to decimal**:
   \[
   11_b = b + 1
   \]

###

Learn how to solve a number system problem involving base conversion and multiplication. Understand the concept of converting numbers from one base to another and solving equations in different bases. Suitable for high school students studying number theory and base systems.

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