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 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.
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.

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.
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Answer 1

To represent the problem described, we need to create an inequality that captures the relationship between 4.5, one-third of a number \( n \), and the limit of 38.9.

We know the following from the problem statement:

1. The sum of 4.5 and one-third of a number should be at most 38.9.
2. The mathematical expression for one-third of a number \( n \) is \( \frac{1}{3}n \).

So we can write the inequality as:

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

Now let's evaluate the options given:

1. Option 1: \( 13n + 4.5 \geq 38.9 \) - This is incorrect as it does not match our inequality.
2. Option 2: \( \frac{1}{3}n + 4.5 \leq 38.9 \) - This is correct.
3. Option 3: \( 13n + 4.5 \leq 38.9 \) - This is incorrect.
4. Option 4: \( \frac{1}{3}n + 4.5 = 38.9 \) - This is incorrect as it represents equality, not an inequality.

Thus, the correct inequality that represents the problem is:

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

Therefore, the response 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.