Answer:
n = 5
Explanation:
Any 3-digit number to the base n will have its rightmost digit have a place value of n⁰, its next rightmost digit a place value of n¹ and the leftmost digit will have a place value of n²
This means 133can be represented as follows
n² n¹ n⁰
1 3 3
The actual value in terms of a base of 10
= 3 x n⁰ + 3 x n¹ + 1 x n²
= 3 x 1 + 3 x n + 1 x n² (n⁰ = 1 and n¹ = n)
= 3 + 3n + 1n²
Since we are given the information that 133ₙ = 43₁₀
3 + 3n + 1n² = 43
subtract 3 from both sides
3n + 1n² = 40
Rewrite as
n² + 3n = 40
Factoring n on the left side=>
n(n + 3) = 40
If we look at the factors of 40:
1 x 40
2 x 20
4 x 10
5 x 8
5 and 8 satisfy the condition n(n + 3) = 40
So n = 5