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Chapter 6: Problem 308

In the following exercises, translate to a proportion. What percent of 85 is 17\(?\)

Short Answer

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Step by step solution

01

Understand the problem

The question is asking to find what percent (let's call it \( x \)) of 85 is 17. This can be set up as the equation: 85 times \( x \) equals 17.
02

Set up the proportion

To set this up as a proportion, we can write it as: \(\frac{17}{85} = \frac{x}{100}\). In this proportion, 100 represents the percent.
03

Solve the proportion

To solve for \( x \), we can cross-multiply and then divide. First, multiply 17 by 100, which gives 1700. Then, divide 1700 by 85: \(x = \frac{1700}{85}\).
04

Calculate the value of x

Perform the division: \( x = \frac{1700}{85} = 20 \). Therefore, 17 is 20% of 85.

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Key Concepts

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

Translating Percentages into Proportions
Understanding how to translate percentages into proportions is a useful skill. When confronted with a problem asking 'what percent of a number is another number,' we use a proportion. In this scenario, let's denote the unknown percentage as \( x \). To set up a proportion, we can use the relationship:
  • The part (in this case, 17)
  • The whole (in this case, 85)
  • The unknown percent over 100
From here, it becomes simple algebra. The proportion is formatted as \( \frac{part}{whole} = \frac{percent}{100} \), or more specifically \( \frac{17}{85} = \frac{x}{100} \). This equation can then be solved for \( x \).
Understanding Proportions
Proportions are equations that express two ratios as equal. In this context, we're comparing the ratio of a part to its whole with the ratio of a percent to 100. To set it up:
  • Identify the part (17)

  • Identify the whole (85)

  • Use 100 as the percent denominator

So, we set up the equation: \( \frac{17}{85} = \frac{x}{100} \). To solve for \( x \), we cross-multiply:
\( 17 \times 100 = 85 \times x \)
Then, we divide by the whole:
\( x = \frac{1700}{85} \)
Solving this, we find \( x \), which tells us the percentage equivalent.
Problem-Solving Tactics
Solving percentage problems involves regular problem-solving tactics. Let's break down the approach:
  • Read the problem carefully
  • Identify what is being asked and the given numbers
  • Set up the proportion
  • Solve the proportion
  • Re-check your solution for accuracy

For our example: 'What percent of 85 is 17?'
Step 1: Identify the part (17) and the whole (85).
Step 2: Set it up as \( \frac{17}{85} = \frac{x}{100} \).
Step 3: Cross-multiply and solve for \( x \).
Step 4: Perform the division \( x = \frac{1700}{85} \).

Problem-solving becomes intuitive with practice. Remember to break down each step and double-check your answers.

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