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?(1 point)

Question

Responses

1/3n+4.5≤38.9
, where n
is equal to the number.
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.

1/3n+4.5=38.9
, where n
is equal to the number.
Start Fraction 1 over 3 end fraction n plus 4.5 equals 38.9 , where n is equal to the number.

4.5+1/3+n≤38.9
, where n
is equal to the number.
4.5 plus Start Fraction 1 over 3 end fraction plus n less than or equal to 38.9 , where n is equal to the number.

1/3n+4.5≥38.9
, where n
is equal to the number.

Answer 1

The correct inequality to represent the problem is:

\[ \frac{1}{3}n + 4.5 \leq 38.9 \]

This states that the sum of one-third of a number \( n \) and 4.5 is equal to at most 38.9.

From this inequality, we can solve for \( n \) to find all possible values of the number.

To solve the inequality, follow these steps:

1. Subtract 4.5 from both sides:

\[ \frac{1}{3}n \leq 38.9 - 4.5 \]

\[ \frac{1}{3}n \leq 34.4 \]

2. Multiply both sides by 3:

\[ n \leq 34.4 \times 3 \]

\[ n \leq 103.2 \]

So the solution set for \( n \) is:

\[ n \leq 103.2 \]

Therefore, the possible values of the number \( n \) are all numbers less than or equal to 103.2.