To solve the problem, we need to express the relationship given: "the sum of 4.5 and one-third of a number is equal to at most 38.9."
This can be translated into mathematical terms as follows:
- "One-third of a number" can be represented as \(\frac{1}{3}n\).
- The sum of 4.5 and this one-third of a number is at most 38.9, which means it is less than or equal to 38.9.
Therefore, we can express this as the inequality:
\[ \frac{1}{3}n + 4.5 \leq 38.9 \]
So the correct option to represent the inequality is:
\(\frac{1}{3}n + 4.5 \leq 38.9\), where \(n\) is equal to the number.
Now, to find all the possible values of \(n\), we can solve the inequality:
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Subtract 4.5 from both sides: \[ \frac{1}{3}n \leq 38.9 - 4.5 \] \[ \frac{1}{3}n \leq 34.4 \]
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Multiply both sides by 3 to isolate \(n\): \[ n \leq 34.4 \times 3 \] \[ n \leq 103.2 \]
Thus, the solution set for \(n\) is \(n \leq 103.2\).
In conclusion, the inequality to use is: \[ \frac{1}{3}n + 4.5 \leq 38.9 \] And the possible values for \(n\) are all real numbers such that \(n \leq 103.2\).
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