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Chapter 6: Problem 2

Translate to an equation. Do not solve. \(98 \%\) of 57 is what?

Short Answer

Expert verified
\[0.98 \times 57 = x\]

Step by step solution

01

Understand the Problem

We need to translate the sentence '98% of 57 is what?' into a mathematical equation.
02

Identify the Components

The phrase '98% of 57' indicates a percentage operation. The word 'is' indicates equality. The word 'what' represents an unknown value, which we can denote as x.
03

Convert the Percentage

Convert 98% to its decimal form. Remember that 98% is equivalent to 0.98 in decimal form, because percent means 'per hundred'.
04

Write the Equation

Combine the decimal form of the percentage with the value 57 and set it equal to x. The equation is: \[0.98 \times 57 = x\]

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Key Concepts

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

Translating Sentences to Equations
When faced with word problems in math, it's crucial to translate the sentences into mathematical equations. This process involves identifying key phrases and terms that indicate mathematical operations. For example, the phrase 'of' often indicates multiplication, while the word 'is' signifies equality. In the problem '98% of 57 is what?', we recognize that '98% of 57' involves multiplying 57 by 98%. We use the word 'what' to represent an unknown variable, typically denoted by x. Thus, we translate the sentence into the equation: \(0.98 \times 57 = x\).
Converting Percentages to Decimals
To solve problems involving percentages, you must convert the percentage to a decimal. Percentages are based on the number 100, so you divide the percentage by 100 to get its decimal form. For instance, 98% is written as: \[ 98 \frac{per}{100} = 0.98 \]. This decimal form makes it easier to use in mathematical equations. Converting percentages to decimals is a fundamental skill in both algebra and everyday calculations.
Unknown Variables
In many math problems, especially algebra, you come across unknown values that you need to find. These unknown values are represented by variables like x. In the sentence '98% of 57 is what?', the word 'what' is our unknown value. Representing unknowns with variables helps to create a clear and solvable equation. Here, we denote the unknown with x, giving us the equation: \(0.98 \times 57 = x\). This way, we can later solve for x to find the answer.

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Most popular questions from this chapter

In baseball, the strike zone is normally a 17 -in. by 30 -in. rectangle. Some batters give the pitcher an advantage by swinging at pitches thrown out of the strike zone. By what percent is the area of the strike zone increased if a 2 -in. border is added to the outside?

Convert to decimal notation. \(\frac{18}{102}\)

A lab technician has \(540 \mathrm{~mL}\) of a solution of alcohol and water; \(8 \%\) is alcohol. How many milliliters are alcohol? water?

Solve: \(x+\frac{2}{5}=\frac{9}{10}\).

Solve. The sales tax rate in Miami, Florida, is \(1 \%\) for Dade County plus \(6 \%\) for the state. Find the total amount paid for 2 tires at \(\$ 49.95\) each.
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