Problem 55 - Elementary Algebra

Question

Answer the question by setting up and solving an appropriate equation. What is \(120 \%\) of 50 ?

Step-by-Step Solution

Answer

120% of 50 is 60.

Step 1: Understand the Problem

The problem is asking for 120% of the number 50. In mathematical terms, 'percent' means 'per hundred,' so 120% can be interpreted as 120 out of 100, or 1.2 in decimal form.

Step 2: Convert Percentage to Decimal

To convert 120% to a decimal, you divide by 100. Thus, you have \( 120 \% = 1.2 \).

Step 3: Set Up the Equation

Create an equation to solve for 120% of 50 using the decimal you found: \( x = 1.2 \times 50 \).

Step 4: Solve the Equation

Perform the multiplication: \( x = 1.2 \times 50 = 60 \). This tells us that 120% of 50 equals 60.

Step 5: Verify the Solution

Check that the calculations are correct by considering that 1.2 times 50 indeed equals 60, confirming the solution.

Key Concepts

Equation Solving

Equation solving is a pivotal concept in mathematics that involves finding the value of an unknown variable that satisfies a given condition. In our problem, we're tasked with finding what 120% of 50 is. This requires setting up an equation where the unknown variable, often represented as \( x \), represents the solution to the problem at hand. The equation is formulated based on the relationship described by the problem statement.
Here's a clear process to solve an equation:

• Identify the unknown quantity you need to find, in this case, the 120% of 50.
• Translate the word problem into a mathematical equation. For this example, it would be \( x = 1.2 \times 50 \).
• Solve the equation by performing the necessary mathematical operations. Here, multiply 1.2 by 50 to find \( x = 60 \).

This simple approach to equation solving can be applied to different types of problems, helping you to systematically tackle problems by breaking them down into achievable parts.

Decimal Conversion

Decimal conversion is critical when dealing with percentages in math. It involves translating a percentage into a decimal format, simplifying the calculation processes. Percentages are fractions of 100, meaning 120% is equivalent to 120 out of 100, which translates to 1.2 in decimal form.
To convert any percentage to a decimal:

• Take the percentage number and divide it by 100.
• For instance, to convert 120%, perform the division: \( \frac{120}{100} = 1.2 \).
• Use this decimal in computations, such as equations, to make calculations easier.

This process is essential for solving many mathematical problems, especially those involving equations, as having numbers in decimal form can simplify multiplication and division.

Mathematical Problem Solving

Mathematical problem solving involves understanding the problem, devising a plan to address it, carrying out the plan, and then verifying that the problem is correctly solved. In our present scenario, we're asked to calculate 120% of 50, which encompasses all these steps effectively.
Here’s how to approach this problem:

• Understanding: Recognize that 120% means 120 per 100, and thus you're looking to find this relation with the number 50.
• Planning: Convert this percentage into a decimal for simplicity, resulting in 1.2.
• Executing: Formulate the equation \( x = 1.2 \times 50 \) and solve it to find \( x = 60 \).
• Verification: A quick recalculation or simple check assures that multiplying 50 by 1.2 indeed results in 60, confirming the correctness.

This structured approach ensures a comprehensive understanding and accurate solution of mathematical problems, enhancing problem-solving skills.