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------------------------------------------------ The sum of 4.6 and one-third of a number is equal to at most 39.1. What are all the possible values of the number?

Artem wrote the inequality [tex]\frac{1}{3} n + 4.6 \leq 39.1[/tex], where [tex]n[/tex] equals the number, to help solve this problem. Solve his inequality.

A. [tex]n \leq 103.5[/tex]
B. [tex]n \leq 112.7[/tex]
C. [tex]n \leq 131.1[/tex]
D. [tex]n \leq 11.5[/tex]

To solve the inequality [tex]$\frac{1}{3}n + 4.6 \leq 39.1$[/tex], we need to determine the possible values for the variable [tex]$n$[/tex].

Here’s a step-by-step solution:

1. Start with the given inequality:
[tex]\[
\frac{1}{3}n + 4.6 \leq 39.1
\][/tex]

2. Subtract 4.6 from both sides to isolate the term with [tex]$n$[/tex]:
[tex]\[
\frac{1}{3}n \leq 39.1 - 4.6
\][/tex]

3. Calculate the right side of the inequality:
[tex]\[
39.1 - 4.6 = 34.5
\][/tex]

So now the inequality is:
[tex]\[
\frac{1}{3}n \leq 34.5
\][/tex]

4. Multiply both sides by 3 to solve for [tex]$n$[/tex]:
[tex]\[
n \leq 34.5 \times 3
\][/tex]

5. Calculate the result:
[tex]\[
n \leq 103.5
\][/tex]

So, the possible values for the number [tex]$n$[/tex] are all the numbers that are less than or equal to 103.5. Therefore, the correct answer is [tex]$n \leq 103.5$[/tex].