Answer :
Sure! Let's go through the problem step-by-step to find the right equation.
Problem:
A number, [tex]\( n \)[/tex], is added to 15 less than 3 times itself. The result is 101. Which equation can be used to find the value of [tex]\( n \)[/tex]?
Step 1: Understand the problem.
- We have a number [tex]\( n \)[/tex].
- We need to add [tex]\( n \)[/tex] to 15 less than 3 times [tex]\( n \)[/tex].
- The result of this operation should be 101.
Step 2: Translate the words into a mathematical equation.
1. "3 times [tex]\( n \)[/tex]" means [tex]\( 3n \)[/tex].
2. "15 less than 3 times [tex]\( n \)[/tex]" means [tex]\( 3n - 15 \)[/tex].
3. "A number, [tex]\( n \)[/tex], is added to 15 less than 3 times itself" means [tex]\( n + (3n - 15) \)[/tex].
Step 3: Set up the equation.
According to the problem, the sum of [tex]\( n \)[/tex] and [tex]\( 3n - 15 \)[/tex] should equal to 101:
[tex]\[ n + (3n - 15) = 101. \][/tex]
Step 4: Simplify the equation.
Let's simplify [tex]\( n + (3n - 15) \)[/tex]:
[tex]\[ n + 3n - 15 = 101. \][/tex]
Combine like terms:
[tex]\[ 4n - 15 = 101. \][/tex]
Step 5: Look at the provided choices and identify the correct one.
The provided choices are:
1. [tex]\( 3n - 15 + n = 101 \)[/tex]
2. [tex]\( 3n + 15 + n = 101 \)[/tex]
3. [tex]\( 3n - 15 - n = 101 \)[/tex]
4. [tex]\( 3n + 15 - n = 101 \)[/tex]
The simplified version of the equation [tex]\( n + (3n - 15) = 101 \)[/tex] is written as:
[tex]\[ 3n - 15 + n = 101. \][/tex]
So, the correct equation from the given choices is:
[tex]\[ 3n - 15 + n = 101. \][/tex]
This is choice 1.
Problem:
A number, [tex]\( n \)[/tex], is added to 15 less than 3 times itself. The result is 101. Which equation can be used to find the value of [tex]\( n \)[/tex]?
Step 1: Understand the problem.
- We have a number [tex]\( n \)[/tex].
- We need to add [tex]\( n \)[/tex] to 15 less than 3 times [tex]\( n \)[/tex].
- The result of this operation should be 101.
Step 2: Translate the words into a mathematical equation.
1. "3 times [tex]\( n \)[/tex]" means [tex]\( 3n \)[/tex].
2. "15 less than 3 times [tex]\( n \)[/tex]" means [tex]\( 3n - 15 \)[/tex].
3. "A number, [tex]\( n \)[/tex], is added to 15 less than 3 times itself" means [tex]\( n + (3n - 15) \)[/tex].
Step 3: Set up the equation.
According to the problem, the sum of [tex]\( n \)[/tex] and [tex]\( 3n - 15 \)[/tex] should equal to 101:
[tex]\[ n + (3n - 15) = 101. \][/tex]
Step 4: Simplify the equation.
Let's simplify [tex]\( n + (3n - 15) \)[/tex]:
[tex]\[ n + 3n - 15 = 101. \][/tex]
Combine like terms:
[tex]\[ 4n - 15 = 101. \][/tex]
Step 5: Look at the provided choices and identify the correct one.
The provided choices are:
1. [tex]\( 3n - 15 + n = 101 \)[/tex]
2. [tex]\( 3n + 15 + n = 101 \)[/tex]
3. [tex]\( 3n - 15 - n = 101 \)[/tex]
4. [tex]\( 3n + 15 - n = 101 \)[/tex]
The simplified version of the equation [tex]\( n + (3n - 15) = 101 \)[/tex] is written as:
[tex]\[ 3n - 15 + n = 101. \][/tex]
So, the correct equation from the given choices is:
[tex]\[ 3n - 15 + n = 101. \][/tex]
This is choice 1.
