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?

Question

A. 1/5n + 4.5 > 38.9, where n is equal to the number.
B. 4.5 + 1/3 + n < 38.9, where n is equal to the number.
C. 1/3n + 4.5 = 38.9, where n is equal to the number.
D. 1/3n + 4.5 < 38.9, where n is equal to the number.

Answer 1

To solve the problem, let's define the number as $n$.

We need to express the relationship given in the problem mathematically. The problem states that the sum of 4.5 and one-third of the number is at most 38.9.

Mathematically, this can be written as:
$$4.5+\frac{1}{3}n\le 38.9$$

Now, let's match this inequality with the options provided:
- Option A: $\frac{1}{5}n+4.5>38.9$
This is incorrect because it does not match the requirement given in the problem.

- Option B: $4.5+\frac{1}{3}+n<38.9$
This is incorrect because it incorrectly adds one-third directly, and does not match the requirement correctly.

- Option C: $\frac{1}{3}n+4.5=38.9$
This is incorrect because it considers the relationship as an equality rather than an inequality.

- Option D: $\frac{1}{3}n+4.5<38.9$
This is the closest option but note the problem stated "at most" which implies $\le$. Hence it should ideally be $\le$.

However, based on the options given, there is no perfect match, but Option D is the most reasonable choice and would ideally be $\frac{1}{3}n+4.5\le 38.9$.

Next, solving for $n$:
$$\frac{1}{3}n+4.5\le 38.9$$

First, subtract 4.5 from both sides:
$$\frac{1}{3}n\le 38.9-4.5$$
$$\frac{1}{3}n\le 34.4$$

Then, multiply both sides by 3:
$$n\le 34.4\times 3$$
$$n\le 103.2$$

So, the possible values of the number $n$ are:
$$n\le 103.2$$

The correct inequality to solve would ideally be: $\frac{1}{3}n+4.5\le 38.9$.

Answer 2

CHOOSE ONE THAT IS THE CLOSEST TO THE CORRECT ANSWER

Answer 3

Given the choices and the need to choose the closest one to the correct inequality, the best option would be:

D. $\frac{1}{3}n+4.5<38.9$

Even though it uses "<" instead of "≤", it is the closest representation of the relationship described in the problem.