Problem 16 - 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. Three times the sum of five and a number is \(48 .\) Find the number.

Step-by-Step Solution

Answer

The solution to the equation is \(x = 11\).

Step 1: Setting up the equation

From the problem, it is known that three times the sum of five and a number is 48. This can be expressed as an equation: \(3 * (5 + x) = 48.\)

Step 2: Simplifying the equation

By performing the multiplication, the equation can be simplified to: \(15 + 3x = 48.\)

Step 3: Rearranging the equation to solve for x

The goal is to get \(x\) by itself on one side of the equation. Subtract \(15\) from both sides of the equation in order to isolate \(3x\): \(3x = 48 - 15\)

Step 4: Simplifying the equation

Performing the subtraction simplifies the equation to: \(3x = 33.\)

Step 5: Solving for x

Divide both sides of the equation by 3 to solve for \(x\): \(x = 33 / 3\)