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Chapter 6: Problem 15

Translate to an equation and solve. \(\$ 39\) is what percent of \(\$ 50 ?\)

Short Answer

Expert verified
39 is 78% of 50.

Step by step solution

01

Understand the Problem

We need to find what percent of 50 is 39. This involves finding the percentage.
02

Set Up the Equation

To find the percentage, let's use the formula: \[ \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100 \]Here, the part is 39 and the whole is 50. Therefore, the equation becomes: \[ \text{Percentage} = \frac{39}{50} \times 100 \]
03

Calculate the Fraction

Divide 39 by 50: \[ \frac{39}{50} = 0.78 \]
04

Convert to a Percentage

Now multiply by 100 to convert the decimal to a percentage: \[ 0.78 \times 100 = 78 \]
05

State the Answer

Therefore, 39 is 78% of 50.

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Key Concepts

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

percentage formula
When working with percentages, we use a specific formula to find the desired values. This formula is: \( \text{Percentage} = \frac{\text{Part}}{\text{Whole}} \times 100 \). Here鈥檚 a breakdown of the components:
  • Part: This is the number you need to find the percentage of. In the given exercise, it is 39.
  • Whole: This is the total or whole number, which is 50 in this case.
  • 100: This number is standard in percentage calculations and converts the fraction into a percentage.
Plug the numbers into the formula: \( \frac{39}{50} \times 100 = 78\% \). This tells us that 39 is 78% of 50.
basic arithmetic
The foundation of solving percentage problems is basic arithmetic. Let's break down the arithmetic concepts involved:
  • Division: To find out what fraction 39 is of 50, we divide 39 by 50. This gives us \( \frac{39}{50} = 0.78 \).
  • Multiplication: After finding the decimal value, we multiply by 100 to convert it to a percentage. Therefore, \( 0.78 \times 100 = 78\% \).
These simple operations鈥攄ivision to find the decimal and multiplication to find the percentage鈥攁re critical steps you鈥檒l find yourself using frequently in many math problems.
solving equations
In the given exercise, solving the problem involves translating the word problem into an equation and then solving it step-by-step. Here's a breakdown:
First, understand the problem statement: '39 is what percent of 50?'
Step 1: Write the equation using the percentage formula: \( \text{Percentage} = \frac{39}{50} \times 100 \).
Step 2: Perform the division: \( \frac{39}{50} = 0.78 \).
Step 3: Convert this decimal to a percentage by multiplying by 100: \( 0.78 \times 100 = 78\% \).
Finally, state the answer: 39 is 78% of 50. This logical sequence of setting up and solving equations is effective in breaking down and understanding various math problems.

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