Question

Match the percent problem with the equation that represents it. A. \(a=(0.39)(50)\) B. \(39=p(50)\) C. \(39=0.50 b\) \(39 \%\) of 50 is what number?

Short answer

The matching equation for the problem '39% of 50 is what number?' is equation A: \(a= (0.39)(50)\).

Step-by-step solution

Identify the components of the problem

The problem '39% of 50 is what number?' consists of three components. The fraction represented by the percentage (39%), the number '50' which the percentage is taken of, and 'what number', representing the unknown value we want to find.

Translate percentage into decimal form

The percentage 39% can be transformed into decimal form by dividing the number by 100. This gives us 0.39.

Formulate the problem as an equation

The phrase '39% of 50 is what number?' can be translated into an equation, where 'of' suggests multiplication, and 'is' suggests the equal sign. Transforming the percentage into decimal form, we get the equation \(a = (0.39)(50)\).

Identify matching equation

Looking at the provided equations, equation A: \(a = (0.39)(50)\), matches the formulated equation from the problem.

Key concepts

Translating Percentages to Decimals

Understanding how to translate percentages into decimals is a fundamental skill in mathematics. It's a simple conversion process, but a powerful tool when dealing with percentage problems. A percentage is a way of expressing a number as a fraction of 100. To convert a percentage to a decimal, you simply divide it by 100. For example, to convert 39% to a decimal, divide 39 by 100 to get 0.39.

Why is this important? Once you have a decimal, it's much easier to perform arithmetic operations like multiplication or division. In our example, 39% is the same as 0.39, and now we're ready to use that number in further calculations. Remember, moving the decimal two places to the left is an easy shortcut for this conversion!

Formulating Equations

Formulating equations is a crucial step in solving mathematical problems, especially when dealing with percentages. An equation is essentially a statement that two expressions are equal. To create an equation from a word problem, identify what value you're solving for — this will be your variable, often represented by letters such as 'a', 'b', or 'x'.

In our example problem, '39% of 50 is what number?', we're looking for a specific value that arises from taking 39% of 50. By converting the percentage to a decimal and interpreting 'of' as multiplication and 'is' as the equals sign, we create the equation, which in this case is \( a = (0.39)(50) \). This equation clearly states that some number 'a' is equal to 39% of 50—the core of our problem.

Percentage of a Number

Finding the percentage of a number is a common task in math that involves multiplicative comparison. Essentially, you're determining how much one number is as a fraction of another number. To calculate this, first convert the percentage to a decimal. Then multiply that decimal by the number you want to find the percentage of.

Let's apply this to our textbook problem: to find what 39% of 50 is, we convert 39% to 0.39 and multiply it by 50. The operation can be visualized as \( 0.39 \times 50 = a \), where 'a' will be our final answer. Going through these steps, we see how percentage problems can be broken down and solved methodically, leading to a better understanding of the concept and the correct answer.