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Chapter 2: Problem 6

Find each number described. See Examples I and 2. The number 126 is \(35 \%\) of what number?

Short Answer

Expert verified
The number is 360.

Step by step solution

01

Identify What is Given

We know that 126 is given as \(35\%\) of some unknown number. Let's denote the unknown number as \(x\).
02

Convert Percentage to Decimal

To solve the problem, convert \(35\%\) to a decimal by dividing by 100. This gives us \(0.35\).
03

Set Up the Equation

The equation that represents the problem is: \(0.35 \times x = 126\). This is because \(35\%\) of the number \(x\) is equal to 126.
04

Solve for \(x\)

To find \(x\), divide both sides of the equation by \(0.35\). Thus, \(x = \frac{126}{0.35}\).
05

Compute the Result

Carry out the division \(x = \frac{126}{0.35} = 360\). This calculation gives us the original number.

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Key Concepts

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

Understanding Algebra
Algebra is like the language of mathematics. It provides us the tools needed to express general relationships and patterns using symbols and letters.
In the exercise, we use algebra to represent the unknown number with the symbol \(x\). This makes it easier to write equations that can be solved.
Key points about algebra include:
  • Using symbols, often letters, to represent unknown values or variables.
  • Writing equations to show mathematical relationships.
  • Manipulating these equations to find the value of unknowns.
Algebra helps us not only in solving specific problems but also in understanding how different quantities relate to each other.
Solving Equations in Steps
Solving equations can feel like breaking down a mystery. The goal is to find the value of the unknown variable.
In our problem, the key equation is \(0.35 \times x = 126\). This equation was created from understanding the phrase 鈥�126 is 35% of what number?鈥滺ere's how we solve it step-by-step:
  • Recognize what is given and what you need to find: Here, we want to find \(x\).
  • Convert percentages into decimals, simplifying the math: \(35\%\) becomes \(0.35\).
  • Set up the equation using our understanding of percentages.
  • Isolate the variable by using algebraic operations: To solve for \(x\), divide both sides by \(0.35\).
  • Calculate the result to discover the value: Solve \(x = \frac{126}{0.35} = 360\).
This systematic approach ensures clarity and accuracy, leading us directly to the solution.
Importance of Mathematics Education
Mathematics education is a cornerstone in developing logical thinking and problem-solving skills.
It not only prepares students for academic success but also enhances their ability to navigate daily life challenges. Through math education, learners develop:
  • Critical thinking skills: Recognizing patterns, evaluating solutions, and reasoning through complexity.
  • Practical skills: Calculating percentages like in our example can be essential for everyday tasks such as shopping and managing finances.
  • Adaptability: Applying mathematical principles to new and varied contexts beyond traditional math problems.
By gaining a deeper understanding of concepts such as algebra and equations, students build confidence and intellectual curiosity that benefits lifelong learning and decision-making.

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Most popular questions from this chapter

Must the percents in a circle graph have a sum of \(100 \% ?\) Why or why not?

In 1971, T. Theodore Fujita created the Fujita Scale (or F Scale), which uses ratings from 0 to 5 to classify tornadoes, based on the damage that wind intensity causes to structures as the tornado passes through. This scale was updated by meteorologists and wind engineers working for the National Oceanic and Atmospheric Administration (NOAA) and implemented in February 2007 . This new scale is called the Enhanced \(\mathrm{F}\) Scale. An EF-0 tornado has wind speeds between 65 and \(85 \mathrm{mph}\), inclusive. The winds in an EF-1 tornado range from 86 to \(110 \mathrm{mph}\). In an EF- 2 tornado, winds are from 111 to \(135 \mathrm{mph}\). An EF- 3 tornado has wind speeds ranging from 136 to \(165 \mathrm{mph} .\) Wind speeds in an EF- 4 tornado are clocked at 166 to \(200 \mathrm{mph}\). The most violent tornadoes are ranked at EF-5, with wind speeds of at least 201 mph. (Source: Storm Prediction Center, NOAA) Letting \(y\) represent a tornado's wind speed, write a series of six inequalities that describe the wind speed ranges corresponding to each Enhanced Fujita Scale rank.

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