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Let's represent the unknown number as 'x'.
According to the problem, the sum of 4.5 and one third of the number (x) is equal to at most 38.9. This can be expressed as follows:
4.5 + (1/3)x ≤ 38.9
To solve this inequality, we can multiply both sides of the inequality by 3 to eliminate the fraction:
3(4.5 + (1/3)x) ≤ 3(38.9)
After simplifying, we get:
13.5 + x ≤ 116.7
Now, let's solve for x:
x ≤ 116.7 - 13.5
x ≤ 103.2
Therefore, the possible values of x are any real numbers less than or equal to 103.2.