The sum of 4.6 and one-third a number is equal to at most 39.1. What are all the possible values of the number? Artem wrote the inequality 13n+4.6≤39.1

Question

, where n equals the number, to help solve this problem. Solve his inequality.(1 point)
Responses

n≤131.1
n less than or equal to 131.1

n≤11.5
n less than or equal to 11.5

n≤103.5
n less than or equal to 103.5

n≤112.7

Answer 1

Let's solve the inequality that Artem wrote:

\[ 13n + 4.6 \leq 39.1 \]

First, we need to isolate \( n \):

1. Subtract \( 4.6 \) from both sides:

\[ 13n \leq 39.1 - 4.6 \]

2. Calculate \( 39.1 - 4.6 \):

\[ 39.1 - 4.6 = 34.5 \]

So, we have:

\[ 13n \leq 34.5 \]

3. Now, divide both sides by \( 13 \):

\[ n \leq \frac{34.5}{13} \]

4. Calculate \( \frac{34.5}{13} \):

\[ \frac{34.5}{13} = 2.6538461538461537 \approx 2.65 \]

So the final result is:

\[ n \leq 2.65 \]

Now let's compare this value with the provided options:

• \( n \leq 131.1 \)
• \( n \leq 11.5 \)
• \( n \leq 103.5 \)
• \( n \leq 112.7 \)

None of these options match the calculated answer, \( n \leq 2.65 \).

There might have been a mistake in the transcription or setup of the original inequality. The correct inequality based on the problem statement that describes the relationship between one-third of the number and a sum with \( 4.6 \) should have been:

\[ \frac{1}{3}n + 4.6 \leq 39.1 \]

If you meant this inequality instead, we would start from:

\[ \frac{1}{3}n + 4.6 \leq 39.1 \]

1. Subtract \( 4.6 \):

\[ \frac{1}{3}n \leq 39.1 - 4.6 \]

2. Calculate \( 39.1 - 4.6 = 34.5 \):

\[ \frac{1}{3}n \leq 34.5 \]

3. Multiply each side by \( 3 \):

\[ n \leq 34.5 \times 3 \]

4. Calculate \( 34.5 \times 3 = 103.5 \):

Thus, you have:

\[ n \leq 103.5 \]

So the correct answer would be:

n ≤ 103.5
n less than or equal to 103.5