Answer :
Sure! Let's solve the problem step-by-step to find the correct equation.
The problem says:
- A number [tex]\( n \)[/tex] is added to 15 less than 3 times itself.
- The result is 101.
Let's break it down:
1. "3 times itself" means [tex]\( 3n \)[/tex].
2. "15 less than 3 times itself" means [tex]\( 3n - 15 \)[/tex].
3. "A number, [tex]\( n \)[/tex], is added to" implies adding [tex]\( n \)[/tex].
Now, we can set up the equation based on the conditions provided:
[tex]\[ n + (3n - 15) = 101 \][/tex]
Let's simplify this:
- Combine like terms: [tex]\( n + 3n = 4n \)[/tex]
- So, the equation becomes: [tex]\( 4n - 15 = 101 \)[/tex].
Now, solve for [tex]\( n \)[/tex]:
1. First, add 15 to both sides of the equation:
[tex]\[ 4n - 15 + 15 = 101 + 15 \][/tex]
[tex]\[ 4n = 116 \][/tex]
2. Then, divide both sides by 4:
[tex]\[ n = \frac{116}{4} \][/tex]
[tex]\[ n = 29 \][/tex]
This tells us [tex]\( n = 29 \)[/tex].
Therefore, the correct equation from the options provided that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
This matches with the first option [tex]\( 3n - 15 + n = 101 \)[/tex].
The problem says:
- A number [tex]\( n \)[/tex] is added to 15 less than 3 times itself.
- The result is 101.
Let's break it down:
1. "3 times itself" means [tex]\( 3n \)[/tex].
2. "15 less than 3 times itself" means [tex]\( 3n - 15 \)[/tex].
3. "A number, [tex]\( n \)[/tex], is added to" implies adding [tex]\( n \)[/tex].
Now, we can set up the equation based on the conditions provided:
[tex]\[ n + (3n - 15) = 101 \][/tex]
Let's simplify this:
- Combine like terms: [tex]\( n + 3n = 4n \)[/tex]
- So, the equation becomes: [tex]\( 4n - 15 = 101 \)[/tex].
Now, solve for [tex]\( n \)[/tex]:
1. First, add 15 to both sides of the equation:
[tex]\[ 4n - 15 + 15 = 101 + 15 \][/tex]
[tex]\[ 4n = 116 \][/tex]
2. Then, divide both sides by 4:
[tex]\[ n = \frac{116}{4} \][/tex]
[tex]\[ n = 29 \][/tex]
This tells us [tex]\( n = 29 \)[/tex].
Therefore, the correct equation from the options provided that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
This matches with the first option [tex]\( 3n - 15 + n = 101 \)[/tex].
