Problem 50 - Elementary Algebra

Question

Answer the question by setting up and solving an appropriate equation. What is \(35 \%\) of 52 ?

Step-by-Step Solution

Answer

18.2

Step 1: Understand the Question

The question asks for 35% of 52. In mathematical terms, '35% of 52' can be translated to 35/100 multiplied by 52.

Step 2: Set Up the Equation

To find 35% of 52, we set up the equation as follows: \[35\% \times 52 = x\]Where \(x\) represents 35% of 52.

Step 3: Convert Percentage to Decimal

Percent means 'per hundred', so we convert 35% to a decimal by dividing by 100:\[35\% = \frac{35}{100} = 0.35\]

Step 4: Substitute and Solve the Equation

Substitute 0.35 into the equation:\[0.35 \times 52 = x\]Now perform the multiplication:\[x = 0.35 \times 52 = 18.2\]

Step 5: Conclusion

Thus, 35% of 52 is 18.2.

Key Concepts

Mathematical Equation

When solving problems that involve percentages, mathematical equations are a powerful tool to translate verbal statements into a form that can be easily calculated. For the problem at hand, we're asked to find 35% of 52. The word "of" in math typically suggests multiplication. Thus, we construct an equation to express the task we need to perform: \( x = 0.35 \times 52 \). In this equation, \( x \) is the unknown value that represents 35% of 52. Setting up equations in this manner allows us to systematically approach and solve percentage questions with clarity.

Decimal Conversion

Understanding percentage as a concept involves knowing that 'percent' means per hundred. Therefore, converting a percentage to a decimal is achieved by dividing it by 100. This conversion is crucial for performing mathematical operations involving percentages. For instance, to convert 35% to a decimal, we compute: \( 35\% = \frac{35}{100} = 0.35 \). This decimal form, 0.35, is then used in calculations, as it makes the math straightforward and uniform across various operations, such as multiplication which is needed in this problem.

Problem-Solving Steps

Approaching percentage problems systematically ensures accuracy and understanding. First, thoroughly understand the problem statement: you need 35% of 52. Then, construct the equation based on your comprehension, translating linguistic expressions to mathematical symbols: \( x = 0.35 \times 52 \). Next, convert percentages to decimals to facilitate easier calculation. Substituting the decimal in the equation, you then perform the multiplication: \( 0.35 \times 52 = 18.2 \). Finally, make sure to conclude your solution confident in the result, confirming every step logically aligns with both the conversion and the computation processes.