Problem 14 - 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. A number increased by 12 is four times the number. Find the number.

Step-by-Step Solution

Answer

The number is 4.

Step 1: Formulate the equation

According to the problem, a number (let's call this number \(x\)) increased by 12 is four times that same number. That can be translated into the following equation: \(x + 12 = 4x\)

Step 2: Rearrange the equation

To find \(x\), first, isolate the variable \(x\) by subtracting \(x\) from both sides of the equation, which gives: \(12 = 4x - x\) or \(12 = 3x\).

Step 3: Solve for \(x\)

Finally, divide both sides of the equation by 3 to find the number: \(x = 12 / 3 = 4\).