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Chapter 6: Problem 109

Translate and solve. 93 is 75% of what number?

Short Answer

Expert verified
The number is 124.

Step by step solution

01

- Understand the problem

You need to find the number that 75% (or three-fourths) of it equals 93.
02

- Set up an equation

Let鈥檚 denote the unknown number as . Since 93 is 75% of the unknown number, we can write the equation: \( 0.75 \times n = 93 \)
03

- Solve for the unknown number

To find , divide both sides of the equation by 0.75: \( n = \frac{93}{0.75} \)
04

- Calculate the result

Perform the division: \( n = 124 \)

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Key Concepts

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

Equation Solving
Equation solving is a fundamental skill in mathematics. It involves finding the value of an unknown variable by using algebraic operations. In our exercise, the unknown variable is the number we are solving for, denoted as \( n \). Here鈥檚 how we approached it:

We started by setting up the equation: 93 is 75% of the number \( n \). In mathematical terms, this is written as \[ 0.75 \times n = 93 \]. Then, to isolate \( n \), we divided both sides of the equation by 0.75, resulting in \[ n = \frac{93}{0.75} \]. This way, we effectively translated the word problem into a solvable mathematical equation.
Understanding Percentages
Percentages are a way of expressing a number as a fraction of 100. To understand percentages, it鈥檚 essential to grasp that 75% represents 75 out of 100, or \( \frac{75}{100} \). This can also be expressed as a decimal, 0.75.

In our example, we needed to find what number 93 is 75% of. This involves reversing the percentage calculation. Typically, to find a percentage of a number, you multiply the number by the percentage (as a decimal). Here, we performed the inverse operation: given 93 as 75%, we converted it into an equation and then divided to find the original number.
Division
Division is one of the basic arithmetic operations that involves splitting a large group into equal smaller groups. In the context of this exercise, division helps us isolate our unknown number \( n \). After setting up our equation \[ 0.75 \times n = 93 \], we divided both sides by 0.75.

This operation, written as \[ n = \frac{93}{0.75} \], gives us the value of \( n \) by dividing 93 by 0.75. Performing this division yields 124, meaning 93 is 75% of 124. Understanding how to effectively use division in algebra is crucial for solving this kind of problem.

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