Question

\(220 \%\) of a number \(X^{\prime}\) is 44 . What is \(44 \%\) of \(^{4} X^{\prime}\) ? (a) 88 (b) \(8.8\) (c) 66 (d) data insufficient

Short answer

Answer: (d) data insufficient

Step-by-step solution

Find the value of X'

We are given that \(220 \%\) of \(X'\) is equal to 44. We can write this as an equation: \(220 \% \times X' = 44\) To find the value of \(X'\), divide both sides of the equation by 220: \(X' = \frac{44}{220 \%}\) Now, convert the percentage to a decimal by dividing 220 by 100: \(X' = \frac{44}{2.2}\) Now, divide 44 by 2.2: \(X' = 20\)

Find the value of 4X'

Now that we have found the value of \(X'\), we can find the value of \(4X'\) by multiplying \(X'\) by 4: \(4X' = 4 \times 20 = 80\)

Calculate 44% of 4X'

Now we need to find \(44 \%\) of \(4X'\). To do this, multiply \(4X'\) by 44%: \(44 \% \times 4X' = 44 \% \times 80\) Convert the percentage to a decimal by dividing 44 by 100: \(0.44 \times 80\) Now, multiply 0.44 by 80: \(0.44 \times 80 = 35.2\) The value of \(44 \%\) of \(4X'\) is 35.2. Since 35.2 is not one of the given options, the correct answer is (d) data insufficient.

Key concepts

Problem-solving

In life and mathematics alike, problem-solving plays a crucial role. When faced with a problem like the one in our exercise, the first step is to understand what is being asked. Break the problem down into smaller steps that are easier to tackle. To determine what 44% of a modified number is, start by identifying the relationship between given numbers and what you need to find. Ask questions like: What do I know? What do I need to find out? And, how can I use what I know to find out what I need? Following a step-by-step approach helps refine techniques applicable to various problems, enhancing overall problem-solving skills.

Basic Algebra

Algebra is a foundational tool in mathematics that allows us to convert words into mathematical equations. This makes it easier to manipulate and find solutions. In this exercise, we need to use algebra to find the original number from a percentage statement. We start by forming an equation from the phrase "220% of X' is 44." This is represented as \(220\% \times X' = 44\). By doing algebraic manipulations, such as converting percentages into decimals and performing operations, we solve for the unknown \(X'\). The key is understanding that algebra helps translate real-world problems into solvable equations, making complex problems easier to handle.

Number Operations

Number operations, such as addition, subtraction, multiplication, and division, are basic yet essential skills in solving mathematical problems. In our particular exercise, we rely heavily on division and multiplication to find unknown values.

• First, convert percentages into decimals because calculations are simplified that way. For example, \(220\%\) becomes 2.2.
• Then, use division to find \(X'\) by dividing \(44\) by \(2.2\).
• Subsequently, multiply to determine \(4X'\) by simply multiplying \(X'\) by 4.
• Finally, to find \(44\%\) of \(4X'\), convert the percentage to a decimal and multiply it by \(4X'\).

Understanding these operations ensures accurate calculations and helps solve percentage problems in a structured manner.