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Chapter 3: Problem 39

If 99 is subtracted from 5 times a number (x) the answer is 1. What is x?

Short Answer

Expert verified
x = 20

Step by step solution

01

- Set Up the Equation

Start by translating the problem into an algebraic equation. The problem states that if 99 is subtracted from 5 times a number, the answer is 1. This can be written as: i.e., 5x - 99 = 1
02

- Isolate the Term with Variable \((x)\)

To isolate the term involving x, we first add 99 to both sides of the equation: \[ 5x - 99 + 99 = 1 + 99 \] Simplifying this, we get: \[ 5x = 100 \]
03

- Solve for x

Next, solve for x by dividing both sides of the equation by 5: \[ \frac{5x}{5} = \frac{100}{5} \] Simplifying this, we get: \[ x = 20 \]
04

- Verify the Solution

Finally, verify the solution by substituting x back into the original equation: \[ 5 * 20 - 99 = 1 \] \[ 100 - 99 = 1 \] Therefore, our solution is correct.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Algebra Problem Solving
Algebra problem solving involves converting real-world statements into mathematical equations that can be solved systematically. This process generally includes:
  • Identifying key information from the problem statement.
  • Translating the information into algebraic expressions and equations.
  • Solving those equations to find the unknown value(s).
For example, in the exercise, the statement 'If 99 is subtracted from 5 times a number, the answer is 1' is translated into the equation: \( 5x - 99 = 1 \). One must first understand how to correctly interpret the problem before proceeding with the steps to solve it. This step is crucial as it lays the foundation for solving the equation correctly, and it allows you to apply algebraic techniques effectively.
Equation Isolation
Equation isolation is the process of manipulating an equation to get the variable term by itself on one side of the equation. This often involves a sequence of operations like addition, subtraction, multiplication, and division to simplify the equation step by step.

In our example, we aim to isolate x from the equation \( 5x - 99 = 1 \). Here’s how we do it:
  • Add 99 to both sides: \[ 5x - 99 + 99 = 1 + 99 \].
  • Simplify the result: \[ 5x = 100 \].
Next, we divide both sides by 5: \[ \frac{5x}{5} = \frac{100}{5} \].
On simplifying, we find \( x = 20 \).
This process gets the variable by itself, making it easy to solve for the unknown.
Math Verification
Math verification ensures that the solution obtained is indeed correct. It involves substituting the found value back into the original equation to check if it satisfies the equation.

In our problem, we found \( x = 20 \). Let's substitute this back into the original equation to verify: \[ 5 * 20 - 99 = 1 \].
  • Calculate \( 5 * 20 = 100 \).
  • Subtract 99 from 100: \[ 100 - 99 = 1 \].
The left-hand side matches the right-hand side of the original equation, confirming our solution is correct.

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