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Chapter 6: Problem 26

Translate to an equation and solve. $$ 100 \% \text { of what is } \$ 74 ? $$

Short Answer

Expert verified
The number is 74.

Step by step solution

01

Understand the Problem

You need to find the number which, when multiplied by 100%, gives $74.
02

Translate into Equation

Let the unknown number be represented by the variable x. Since 100% of x is equal to x, the equation can be written as: \[ x = 74 \]
03

Solve the Equation

The equation is already in the simplest form. Therefore, the solution is: \[ x = 74 \]
04

Verify the Solution

To verify, calculate 100% of 74: 100% of 74 is equal to 1 * 74 = 74, which matches the original problem.

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Key Concepts

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

Equation Solving
Solving equations is a fundamental concept in algebra. It often involves finding the value of an unknown variable. In the given exercise, the equation is x = 74 This simple equation means that 100% of a number is equal to 74. To 'solve' for x, you are essentially looking to isolate the variable (which in this case is already done for you). In more complex scenarios, you might need to perform additional steps such as:
  • Adding or subtracting numbers on both sides of the equation.
  • Multiplying or dividing both sides by a number to isolate the variable.
Always remember, the goal of equation solving is to perform the same operation on both sides of the equation to maintain equality, ultimately isolating the unknown variable on one side.
Percentage Calculations
Percentage calculations involve determining parts of a whole number, expressed as a fraction of 100. In our exercise, we are asked to find 100% of a number that equals \(74, which means we need to understand what percentages represent. A percentage is essentially a ratio compared to 100. For example:
  • 100% of a number means you take the whole number (100% of x = x).
  • 50% of a number means you take half of that number (50% of x = 0.5x).
  • 20% of a number means you take a fifth of that number (20% of x = 0.2x).
In our specific problem, because 100% of any number is the number itself, the solution is straightforward: x = \)74.
Basic Algebra
Algebra is a branch of mathematics that deals with symbols and the rules for manipulating those symbols. In most cases, those symbols represent quantities without fixed values, known as variables. This exercise touches on several basic algebra concepts:
  • Variable Representation: We use x to represent an unknown quantity.
  • Equation Formulation: We translate words into mathematical equations. In this case, '100% of what is $74' becomes 'x = 74'.
  • Simplification: The equation provided is already simplified, meaning no further steps are needed to isolate the variable.
By mastering these basic algebraic skills, you'll be well-prepared to tackle more complex problems that involve multiple variables and operations.

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Most popular questions from this chapter

Solve. The sales tax rate in Pittsburgh, Pennsylvania, is \(1 \%\) for Allegheny County plus \(6 \%\) for the state. Find the total amount paid for 5 NFL tickets at \(\$ 266\) each.

Solve. Joshua earns \(\$ 120\) for selling \(\$ 2400\) worth of television sets. What is the commission rate?

The amount in a savings account increased from $$\$ 200$$ to $$\$ 216 .$$ What was the percent increase?

The effective yield is the yearly rate of simple interest that corresponds to a rate for which interest is compounded two or more times a year. For example, if \(P\) is invested at \(12 \%,\) compounded quarterly, we multiply \(P\) by \((1+0.12 / 4)^{4},\) or \(1.03^{4}\). Since \(1.03^{4} \approx 1.126\), the \(12 \%\) compounded quarterly corresponds to an effective yield of approximately \(12.6 \% .\) In Exercises 47 and \(48,\) find the effective yield for the indicated account. The account pays \(10 \%\) compounded daily.

A person earns $$\$ 43,200$$ one year and receives an \(8 \%\) raise in salary. What is the new salary?
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