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Chapter 3: Problem 84

In the following exercises, translate and solve. What percent of 215 is \(86 ?\)

Short Answer

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Step by step solution

01

Understand the Problem

The question is asking for the percentage of 215 that equals 86. This means finding a number that, when 215 is multiplied by it and then divided by 100, equals 86.
02

Set Up the Equation

Set up the equation in the form: \[ \frac{x}{100} \times 215 = 86 \]
03

Solve for x

Multiply both sides of the equation by 100 to isolate x on one side: \[ x \times 215 = 8600 \] Now, divide both sides by 215 to solve for x: \[ x = \frac{8600}{215} \]
04

Calculate the Solution

Perform the division to find the value of x: \[ x = 40 \] Therefore, 40% of 215 is 86.

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Key Concepts

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

Fraction to Percentage Conversion
Another crucial aspect of this problem is understanding how to convert fractions to percentages. Given a number as part of a whole, you can represent it as a fraction and then convert it to a percentage.
To do this, multiply the fraction by 100. For instance, if you're asked to find what percentage 86 is of 215, you set it up as a fraction: \( \frac{86}{215} \). To convert this to a percentage, multiply by 100: \( \frac{86}{215} \times 100 = 40 \). This confirms our solution, showing that 86 is 40% of 215.
Understanding these conversions between fractions and percentages is key to solving similar problems effectively and ensures a solid grasp of the concept.

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