Question

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) 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 equals 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 less than or equal to 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

To express the given condition—"The sum of 4.5 and one-third a number is equal to at most 38.9"—in mathematical terms, we can write the inequality as:

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

Where \( n \) is the unknown number.

This means you are looking for all values of \( n \) such that when you take one-third of \( n \) and add 4.5, the result does not exceed 38.9.

So the correct response among the options you listed is:

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

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

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

2. Calculate the right side: \[ \frac{1}{3}n \leq 34.4 \]

3. Multiply both sides by 3: \[ n \leq 34.4 \times 3 \]

4. Calculate the final result: \[ n \leq 103.2 \]

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