Problem 32 - Algebra A Combined Function

Question

Solve. If needed, round money amounts to two decimal places and all other amounts to one decimal place. The number 42 is what percent of \(35 ?\)

Step-by-Step Solution

Answer

42 is 120% of 35.

Step 1: Set Up the Problem

To find what percent one number is of another, you can use the formula: \( \text{Percent} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \). Here, the part is 42 and the whole is 35.

Step 2: Plug in the Values

Substitute the given numbers into the formula. \( \text{Percent} = \left( \frac{42}{35} \right) \times 100 \).

Step 3: Perform the Division

Divide 42 by 35. This gives you \( \frac{42}{35} = 1.2 \).

Step 4: Convert to Percentage

Multiply the result from Step 3 by 100 to convert it into a percentage. \( 1.2 \times 100 = 120 \).

Step 5: Answer the Question

The calculated percentage is 120. Thus, 42 is 120% of 35.

Key Concepts

Understanding Mathematical Formulas

Mathematical formulas are essential tools that simplify complex problems by providing a systematic way to solve them. In many mathematical situations, such as calculating percentages, formulas help us avoid confusion. For instance, in the problem where we need to find what percent 42 is of 35, we use a specific formula: \( \text{Percent} = \left( \frac{\text{Part}}{\text{Whole}} \right) \times 100 \). This formula allows efficient computing by establishing a relationship between the part (42), the whole (35), and their percentage representation.

• Step 1: Identify the 'part' and 'whole' from the problem.
• Step 2: Use the formula to set up the relationship between these values.

The formula essentially tells us how many times the whole value fits into the part, then multiplies it by 100 to convert this ratio into a percentage. This method is quick, reliable, and consistent across different scenarios.

The Role of Division in Finding Percentages

Division is at the heart of calculating percentages. In our problem, division helps in comparing two numbers, 42 and 35. We see that by dividing the part by the whole, we get a ratio which is the first step towards finding the percentage.

• First, we take 42 (the part) and divide it by 35 (the whole).
• The result is 1.2, which represents how many times 35 fits into 42.

This division step is crucial because it sets the foundation for converting the ratio into a percentage. If you understand division, you can easily tackle problems that involve percentages because you're essentially working with fractions of a number.

Importance of Multiplication in the Final Step

Once you have the division result, multiplication steps in to complete the conversion of that ratio into a percentage. For our example, after we've divided 42 by 35 to get 1.2, we multiply that result by 100.

• Multiply 1.2 by 100 to convert the decimal into a percentage format.
• The result, 120, means that 42 is 120% of 35.

Multiplication is essential for scaling the decimal value to a percentage, making it easier to interpret and use in practical situations. While division tells us the ratio, only multiplication transforms it into a readable percentage, concluding the process effectively.