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.

Answer 1

To solve this problem, we need to express the given situation as an inequality.

The problem states that the sum of 4.5 and one-third of a number is equal to at most 38.9. This leads us to the following inequality:

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

Therefore, the correct 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.

Now, to find the possible values of \( n \), we can solve the inequality:

1. Subtract 4.5 from both sides: \[ \frac{1}{3}n \leq 38.9 - 4.5 \]

2. Calculate \( 38.9 - 4.5 \): \[ 38.9 - 4.5 = 34.4 \] So the inequality becomes: \[ \frac{1}{3}n \leq 34.4 \]

3. To eliminate the fraction, multiply both sides by 3: \[ n \leq 3 \times 34.4 \]

4. Calculate \( 3 \times 34.4 \): \[ 3 \times 34.4 = 103.2 \]

Thus, the solution to the inequality is: \[ n \leq 103.2 \]

This means that the possible values of the number \( n \) can be any number less than or equal to 103.2.