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Chapter 2: Problem 20

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.

Short Answer

Expert verified
The number x is 16

Step by step solution

01

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.
02

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: \((3x/4) = 12\).
03

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 \(x = 16\).

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