Problem 18 - Introductory Algebra for College Students

Question

Let \(x\) represent the number. Use the given conditions to write an equation. Solve the equation and find the number. Nine times a number is 30 more than three times that number. Find the number.

Step-by-Step Solution

Answer

The number is 5.

Step 1: Understanding the Problem

The problem sets up the following relationship: Nine times a number is 30 more than three times that number. This can be rewritten as: '9 multiplied by some number is equal to 30 added to 3 times the same number'.

Step 2: Formulate an Algebraic Expression

The statement can be converted to an algebraic equation. Remember, the 'number' is represented by \(x\), thus the statement 'Nine times a number is 30 more than three times that number' becomes \(9x = 3x + 30\).

Step 3: Simplify the Equation

To solve for \(x\) you first need to simplify the equation. Do this by subtracting \(3x\) from both sides to isolate \(x\) terms to one side of the equation, resulting in \(9x - 3x = 30\), which simplifies to \(6x = 30\).

Step 4: Solve for \(x\)

Next, divide both sides of the equation by 6 to solve for \(x\), leading to the solution \(x = 30/6 = 5\).