The sum of 4.5 and one-third a number is equal to at most 38.9. What are all the possible values of the number? How would you write an inequality that could be used to solve this problem?
A4.5+1/3+n≤38.9, where n is equal to the number.
B1/3n+4.5≥38.9, where n is equal to the number.
C1/3n+4.5≤38.9, where n is equal to the number.
D1/3n+4.5=38.9, where n is equal to the number.
The correct representation of the given statement as an inequality is:
C) \( \frac{1}{3}n + 4.5 \leq 38.9 \), where \( n \) is equal to the number.
The inequality signifies that one-third of the number \( n \) plus 4.5 must be less than or equal to 38.9. Now, let's find the possible values for \( n \):
\[
\frac{1}{3}n + 4.5 \leq 38.9
\]
Subtract 4.5 from both sides to isolate the term with \( n \):
\[
\frac{1}{3}n \leq 38.9 - 4.5
\]
\[
\frac{1}{3}n \leq 34.4
\]
Now multiply both sides by 3 to solve for \( n \):
\[
n \leq 34.4 \times 3
\]
\[
n \leq 103.2
\]
Therefore, all the possible values for the number \( n \) are those which are less than or equal to 103.2.