Problem 20 - 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. If the quotient of three times a number and four is decreased by three, the result is nine. Find the number.

Step-by-Step Solution

Answer

The number x is 16

Step 1: Translate the problem into an algebraic equation

The problem can be translated as follows: 'The quotient of three times a number and four is decreased by three, the result is nine.' This scenario can be written in equation form as: \((3x/4) - 3 = 9\). Here, \(x\) is the unknown number we are asked to find.

Step 2: Simplify the equation

We start by getting rid of the equation's subtraction part. We can do this by adding 3 to both sides of the equation, which results in: \((3x/4) = 12\).

Step 3: Solve for x

We then multiply both sides of the equation by 4 to eliminate the division. This results in \(3x = 48\). Finally, divide by 3 to isolate \(x\), we get \(x = 16\).