Question
Four students are told to write a mathematical equation for:
5
less than
6
times a number,
n
, is equal to
4
times the sum of the same number and
10
. The table shows each student’s response.
Which student’s response is correct?
Responses
Cole
Cole
Denise
Denise
Javier
Javier
Makayla
5
less than
6
times a number,
n
, is equal to
4
times the sum of the same number and
10
. The table shows each student’s response.
Which student’s response is correct?
Responses
Cole
Cole
Denise
Denise
Javier
Javier
Makayla
Answers
Answered by
GPT-4o mini
To find out which student’s response is correct, we need to translate the statement "5 less than 6 times a number, n, is equal to 4 times the sum of the same number and 10" into a mathematical equation.
Let's break it down:
1. "6 times a number, n" can be written as \(6n\).
2. "5 less than 6 times a number" means we subtract 5 from \(6n\), which gives us \(6n - 5\).
3. "4 times the sum of the same number and 10" can be written as \(4(n + 10)\).
Now we can set up the equation:
\[
6n - 5 = 4(n + 10)
\]
Next, we'll simplify the right side of the equation:
\[
4(n + 10) = 4n + 40
\]
So the complete equation is:
\[
6n - 5 = 4n + 40
\]
Now, let's see if any of the students provided this equation. Here’s what each student likely wrote:
- Cole: \(6n - 5 = 4(n + 10)\)
- Denise: \(6n - 5 = 4n + 40\)
- Javier: Something else (not specified)
- Makayla: Something else (not specified)
To determine the correct student, the correct form of the equation we derived is:
\[
6n - 5 = 4n + 40
\]
Thus, we need to look for any student who might have written this equation or derived it properly. Based on the descriptions:
Assuming Denise, for example, wrote \(6n - 5 = 4n + 40\), that would be the correct response. If none of the other responses match what we determined, then Denise would be the correct answer.
Thus, the correct response among the students is the one that matches the derived equation, which is:
**Denise** (assuming her response matched). If you have the exact responses for Cole, Javier, and Makayla, please provide them for a more definitive answer.
Let's break it down:
1. "6 times a number, n" can be written as \(6n\).
2. "5 less than 6 times a number" means we subtract 5 from \(6n\), which gives us \(6n - 5\).
3. "4 times the sum of the same number and 10" can be written as \(4(n + 10)\).
Now we can set up the equation:
\[
6n - 5 = 4(n + 10)
\]
Next, we'll simplify the right side of the equation:
\[
4(n + 10) = 4n + 40
\]
So the complete equation is:
\[
6n - 5 = 4n + 40
\]
Now, let's see if any of the students provided this equation. Here’s what each student likely wrote:
- Cole: \(6n - 5 = 4(n + 10)\)
- Denise: \(6n - 5 = 4n + 40\)
- Javier: Something else (not specified)
- Makayla: Something else (not specified)
To determine the correct student, the correct form of the equation we derived is:
\[
6n - 5 = 4n + 40
\]
Thus, we need to look for any student who might have written this equation or derived it properly. Based on the descriptions:
Assuming Denise, for example, wrote \(6n - 5 = 4n + 40\), that would be the correct response. If none of the other responses match what we determined, then Denise would be the correct answer.
Thus, the correct response among the students is the one that matches the derived equation, which is:
**Denise** (assuming her response matched). If you have the exact responses for Cole, Javier, and Makayla, please provide them for a more definitive answer.