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

13n+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.

13n+4.5≥38.9
, where n
is equal to the number.
Start Fraction 1 over 3 end fraction n plus 4.5 greater than or equal to 38.9 , where n is equal to the number.

13n+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.

4.5+13+n≤38.9
, where n
is equal to the number.

Answer 1

To solve the problem, we need to express the situation mathematically using an inequality.

The problem states that the sum of 4.5 and one-third of a number \( n \) is equal to at most 38.9. The phrase "at most" indicates that we can consider values less than or equal to 38.9.

1. The sum of 4.5 and one-third of \( n \) can be expressed as: \[ \frac{1}{3}n + 4.5 \]

2. Setting up the inequality as per the problem statement: \[ \frac{1}{3}n + 4.5 \leq 38.9 \]

Therefore, the correct inequality that represents the situation is: \[ \frac{1}{3}n + 4.5 \leq 38.9 \]

This would mean that the correct response is:

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

Next, you can solve this inequality to find all possible values of \( n \):

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 to isolate \( n \): \[ n \leq 34.4 \times 3 \] \[ n \leq 103.2 \]

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