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Chapter 3: Problem 82

In the following exercises, translate and solve. \(12.3 \%\) of what number is \(\$ 92.25 ?\)

Short Answer

Expert verified
\(750\)

Step by step solution

01

Understand the problem

We need to find a number such that 12.3% of it equals $92.25.
02

Translate the problem into an equation

Let's denote the number we need to find as \(x\). The problem statement '12.3% of \(x\) is \(\$92.25\)' can be written as an equation: \[ 0.123 \times x = 92.25 \]
03

Solve the equation

To solve for \(x\), divide both sides of the equation by 0.123: \[ x = \frac{92.25}{0.123} \]
04

Calculate the value

Use a calculator to find the value of \[ x = \frac{92.25}{0.123} \]. This gives \[ x \approx 750 \]

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Key Concepts

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

solving percentage equations
Solving percentage equations involves changing percentages into decimals. This is the key first step. A percentage like 12.3% is the same as 0.123.
Next, when a problem says '12.3% of what number is \(92.25?', we need to create an equation. We denote the unknown number as 饾懃.
Therefore, 12.3% of 饾懃 can be written as 0.123饾懃. The problem now reads: 0.123饾懃 = 92.25. To find 饾懃, you divide both sides of the equation by 0.123:
\
\
\[ x = \frac{92.25}{0.123} \]
\
\
Finally, use a calculator to perform the division and find 饾懃. In this case, 饾懃 鈮� 750. So, 12.3% of 750 is \)92.25.
This process simplifies percentage problems effectively.
basic algebra
Basic algebra helps in solving equations like the percentage problem. Start by understanding the variables and constants in the equation.
The unknown number we need is typically represented as 饾懃, making it easier to form the equation.
In the given problem: \ \ \ \[ 0.123 x = 92.25 \] \ \ \ Here, 0.123 is a constant (the percentage converted into a decimal), and 92.25 is another constant. We solve for 饾懃 (the unknown variable).
\
Follow these basic steps in algebra:
  • Identify the variable (饾懃)
  • Set up the equation
  • Isolate the variable by performing operations on both sides of the equation

In this problem, you isolate 饾懃 by dividing both sides by 0.123. Basic algebra is powerful in solving various equations systematically.
translating word problems
Translating word problems into mathematical equations is a crucial skill.
First, read the problem carefully. Identify the key information and what is being asked.
In our exercise, the phrase '12.3% of what number is $92.25?' gives clues to form the equation. The percentage (12.3%) tells us to use multiplication, and 'of what number' indicates our unknown variable (饾懃).
  • Translate '12.3%' to 0.123 for mathematical convenience.
  • Restate the problem: 0.123饾懃 = 92.25

Now, solve this equation to find the unknown number. By practicing translating word problems frequently, you will develop a keen ability to understand and solve them more efficiently.

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Most popular questions from this chapter

In the following exercises, solve. Cassius drives his boat upstream for 45 minutes. It takes \(\begin{array}{lll}\text { him } & 30 & \text { minutes to return }\end{array}\) downstream. His speed going upstream is three miles per hour slower than his speed going downstream. Find his upstream and downstream speeds.

In the following exercises, solve. Alonzo works as a car detailer. He charges \(\$ 175\) per car. He is planning to move out of his parents' house and rent his first apartment. He will need to pay \(\$ 120\) for application fees, \(\$ 950\) for security deposit, and first and last months' rent at \(\$ 1,140\) per month. He has \(\$ 1,810\) in savings. How many cars must he detail to have enough money to rent the apartment?

In the following exercises, solve using rectangle properties. The length of a rectangle is 85 feet and the width is 45 feet. What is the perimeter?

In the following exercises, solve. Teegan likes to play golf. He has budgeted \(\$ 60\) next month for the driving range. It costs him \(\$ 10.55\) for a bucket of balls each time he goes. What is the maximum number of times he can go to the driving range next month?

In the following exercises, solve. Andre has been offered an entry-level job. The company offered him \(\$ 48,000\) per year plus \(3.5 \%\) of his total sales. Andre knows that the average pay for this job is \(\$ 62,000\). What would Andre's total sales need to be for his pay to be at least as high as the average pay for this job?
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