To formulate the inequality based on the given statement, we need to identify the components:
"The sum of 4.5 and one-third a number is equal to at most 38.9."
We start by representing the unknown number as \( n \). One-third of that number is \( \frac{1}{3}n \).
We can now write the inequality based on the information provided:
\[ 4.5 + \frac{1}{3}n \leq 38.9 \]
Comparing this to the response options given, the correct inequality is:
Start Fraction 1 over 3 end fraction n plus 4.5 less than or equal to 38.9, where n is equal to the number.
Let's confirm that this inequality represents what is stated:
- The left side, \( 4.5 + \frac{1}{3}n \), indicates the sum of 4.5 and one-third of the number.
- The right side of the inequality shows that this sum is less than or equal to 38.9, matching the phrase "equal to at most".
This means that we can express the answer as:
\[ \frac{1}{3}n + 4.5 \leq 38.9 \]
So, the correct response matches the inequality. To find the possible values of \( n \), we would solve this inequality:
\[ \frac{1}{3}n + 4.5 \leq 38.9 \]
Subtracting 4.5 from both sides gives:
\[ \frac{1}{3}n \leq 34.4 \]
Multiplying both sides by 3 yields:
\[ n \leq 103.2 \]
Thus, the possible values of \( n \) are all numbers that are less than or equal to 103.2.