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Chapter 6: Problem 432

In the following exercises, solve the percent problem. 150\(\%\) of what number is 60\(?\)

Short Answer

Expert verified
The number is 40.

Step by step solution

01

Understand the problem

We need to find the number that, when 150% of it is calculated, results in 60.
02

Set up the equation

Let the unknown number be \( x \). We can set up the equation as follows: 150% of \( x \) equals 60 can be written as: \[ 1.5x = 60 \] Note that 150% is the same as 1.5 when converted to a decimal.
03

Solve for \( x \)

To find the value of \( x \), divide both sides of the equation by 1.5: \[ x = \frac{60}{1.5} \] Calculate the division: \[ x = 40 \]
04

Verify your result

To ensure the solution is correct, calculate 150% of 40 and verify that it equals 60: 150% of 40 is: \[ 1.5 \times 40 = 60 \] Since the result matches the given number, the solution is correct.

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Key Concepts

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

Solving Equations
Solving equations is a critical skill in math that helps us find unknown values. In equations involving percentages, the goal is to isolate the unknown variable on one side of the equation. For example, we start with the equation \ 1.5x = 60 \, where 1.5 represents 150% expressed as a decimal.
To isolate \( x \), we divide both sides of the equation by 1.5:
\ x = \frac{60}{1.5}\
This division gives us the value of \( x \), which is the unknown number we were looking for.
Practicing these steps helps build a strong foundation for solving more complex equations in the future.
Percentages
Percentages represent a part of a whole number, expressed out of 100. This concept is widely used in various real-life scenarios like discounts, interest rates, and statistics. In our given problem, we dealt with 150%, which is more than the whole.
To work with percentages in equations, you need to convert the percentage to a decimal. For example, 150% becomes 1.5 because dividing 150 by 100 gives us 1.5.
Using percentages in math involves:
  • Converting percentages to decimals by dividing by 100
  • Multiplying the decimal with the number
  • Setting up equations based on the problem
This approach makes solving percentage problems straightforward and manageable.
Problem-Solving Steps
To solve percent problems effectively, follow a structured approach:
  • Step 1: Understand the Problem
    Comprehend what is being asked. In our case, we need to find a number that, when multiplied by 150%, equals 60.
  • Step 2: Set Up the Equation
    Translate the problem into a mathematical equation like \ 1.5x = 60 \. This step involves converting the percentage to a decimal (150% to 1.5).
  • Step 3: Solve for the Unknown
    Isolate the unknown variable \( x \) by performing the necessary arithmetic operations, like dividing by 1.5.
  • Step 4: Verify Your Solution
    Double-check your answer by substituting it back into the original equation to ensure it works. Here, 150% of 40 should give us 60, confirming our solution is correct.
Following these steps ensures accuracy and helps develop a systematic problem-solving approach.

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