High School

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]?

A. [tex] 3n - 15 + n = 101 [/tex]
B. [tex] 3n + 15 + n = 101 [/tex]
C. [tex] 3n - 15 - n = 101 [/tex]
D. [tex] 3n + 15 - n = 101 [/tex]

Answer :

To solve this problem, let's break down the information given and form an equation.

The problem states that a number [tex]\( n \)[/tex] is added to "15 less than 3 times itself." Let's translate this phrase into a mathematical expression:

1. Three times the number: [tex]\( 3n \)[/tex]
2. 15 less than 3 times the number: [tex]\( 3n - 15 \)[/tex]

When we add the number [tex]\( n \)[/tex] to "15 less than 3 times itself," we get the expression:

[tex]\[
n + (3n - 15)
\][/tex]

According to the problem, this sum equals 101. So, we form the equation:

[tex]\[
n + (3n - 15) = 101
\][/tex]

Now, let's simplify and solve the equation:

1. Simplify the left side:

[tex]\[
n + 3n - 15 = 101
\][/tex]

Combine like terms:

[tex]\[
4n - 15 = 101
\][/tex]

2. Solve for [tex]\( n \)[/tex]:

Add 15 to both sides:

[tex]\[
4n = 116
\][/tex]

Divide both sides by 4:

[tex]\[
n = 29
\][/tex]

Thus, the correct equation that can be used to find [tex]\( n \)[/tex] is:

[tex]\[
3n - 15 + n = 101
\][/tex]

Among the given options, the correct equation is:

[tex]\[
3n - 15 + n = 101
\][/tex]

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