MathXL: Solving Two-Step Equations

Part 1 of 2

Multiple Representations:

Three times a number, added to 8, is 53. Write an equation that you can use to find the number. Let [tex]n[/tex] represent the number.

What is the number?

Write an equation that you can use to find the number. Choose the correct answer below:

A. [tex]3n - 8 = 53[/tex]
B. [tex]8 + 3n = 53[/tex]
C. [tex]3 + 8 = 53[/tex]
D. [tex]8 - 3 = 53[/tex]

Sure! Let's solve the problem step-by-step.

### Problem Statement:
Three times a number, added to 8, is 53. We need to write an equation to represent this situation and solve for the number. Let [tex]\( n \)[/tex] represent the number.

### Step-by-Step Solution:

1. Writing the Equation:
- According to the problem, three times a number ([tex]\( 3n \)[/tex]) added to 8 equals 53.
- The equation can be written as: [tex]\( 3n + 8 = 53 \)[/tex].

2. Isolating the Variable [tex]\( n \)[/tex]:
- To solve for [tex]\( n \)[/tex], we need to get [tex]\( n \)[/tex] by itself on one side of the equation.
- First, we subtract 8 from both sides of the equation to isolate the term with [tex]\( n \)[/tex] on one side:
[tex]\[
3n + 8 - 8 = 53 - 8
\][/tex]
Simplifying this, we get:
[tex]\[
3n = 45
\][/tex]

3. Solving for [tex]\( n \)[/tex]:
- Now that we have [tex]\( 3n = 45 \)[/tex], we need to divide both sides by 3 to solve for [tex]\( n \)[/tex]:
[tex]\[
\frac{3n}{3} = \frac{45}{3}
\][/tex]
Simplifying this, we get:
[tex]\[
n = 15
\][/tex]

### Final Answer:
The number [tex]\( n \)[/tex] is [tex]\( 15 \)[/tex].

So, [tex]\( n = 15 \)[/tex] is the solution to the given equation.