Problem 84 - Elementary Algebra

Question

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

Step-by-Step Solution

Answer

40%

Step 1: 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.

Step 2: Set Up the Equation

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

Step 3: 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: \[ x = \frac{8600}{215} \]

Step 4: Calculate the Solution

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

Key Concepts

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.