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Chapter 6: Problem 363

In the following exercises, translate and solve. 15 is 8\(\%\) of what number?

Short Answer

Expert verified
The number is 187.5.

Step by step solution

01

Define the Problem

We need to find the number (let's call it x) for which 15 is 8% of it.
02

Set Up the Equation

Translate the problem into an equation. Since 15 is 8% of x, we can write it as: 15 = 0.08x
03

Solve for x

To solve for x, divide both sides of the equation by 0.08: \[ x = \frac{15}{0.08} \]
04

Calculate the Result

Calculate the value of x: \[ x = \frac{15}{0.08} = 187.5 \]

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Key Concepts

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

Percentages in Math
Percentages in math are a way to express a number as a part of a whole. When we say 8% (eight percent), we mean 8 out of every 100 parts. To work with percentages: take the percentage value, divide it by 100, and then use this decimal form in equations.
In our exercise, 8% is equivalent to 0.08. Understanding this conversion is crucial for solving percentage problems.
Equation Solving
Equations allow us to represent and solve problems mathematically. In our exercise, we translated the statement '15 is 8% of what number?' into an equation: 15 = 0.08x. Here, the goal is to find the value of 'x'.
By isolating 'x' on one side, we solve for it. This process involves division: \( x = \frac{15}{0.08} \). Performing this division gives us the answer. Understanding how to manipulate and solve equations is essential for many math problems.
Basic Arithmetic Calculations
Basic arithmetic calculations, like addition, subtraction, multiplication, and division, are fundamental in solving more complex math problems. In our example, the key calculation was division: \( x = \frac{15}{0.08} \).
Understanding and performing these basic operations accurately ensures success in more advanced mathematical tasks. Arithmetic skills form the backbone of problem-solving in math.

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Most popular questions from this chapter

In the following exercises, solve the percent problem. Kyle bought a bicycle in Denver where the sales tax was 7.72\(\%\) of the purchase price. The purchase price of the bicycle was \(\$ 600\) . What was the total cost?

In one month, the median home price in the Northeast rose from \(\$ 225,400\) to \(\$ 241,500\) . Find the percent increase. (Round to the nearest tenth of a percent.)

Solve the applications of percents. Geneva treated her parents to dinner at their favorite restaurant. The bill was $74.25. She wants to leave 16% of the total bill as a tip. How much should the tip be?

In the following exercises, write each sentence as a proportion. \(\$ 7.35\) for 15 ounces is the same as \(\$ 2.94\) for 6 ounces.

In the following exercises, find the rate of commission. Ruben received \(\$ 675\) commission when he sold a \(\$ 4,500\) painting at the art gallery where he works. What was the rate of commission?
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