200% of __ is 26.
The Correct Answer and Explanation is:
To find out what number 200% of is equal to 26, we can set up the problem as follows:
Let ( x ) be the unknown number. Since 200% can be converted into a decimal for calculations, we know that 200% equals 2. Therefore, we can express the relationship mathematically:
[
200\% \text{ of } x = 26
]
This can be rewritten as:
[
2 \cdot x = 26
]
To solve for ( x ), we can divide both sides of the equation by 2:
[
x = \frac{26}{2}
]
Calculating this gives:
[
x = 13
]
So, the correct answer is that 200% of 13 is 26.
Explanation:
Understanding percentages is crucial in various mathematical and real-life applications, from finance to statistics. A percentage represents a fraction out of 100. When we say “200%,” we are referring to double the whole or twice the value. In this case, we want to find a number such that if we take 200% of it, we arrive at 26.
The process of calculating percentages involves converting the percentage into a decimal. For instance, 200% becomes 2. This conversion is important because it allows us to work with whole numbers and simplifies the calculations. The relationship established, ( 2 \cdot x = 26 ), signifies that ( x ) is a number that, when doubled, equals 26.
By isolating ( x ) through division, we can find that ( x = 13 ). This means that if we take 13 and find 200% of it (which is ( 2 \cdot 13 = 26 )), we get the target number of 26. This calculation not only illustrates the relationship between percentages and whole numbers but also reinforces the mathematical operations of multiplication and division, which are fundamental in solving similar problems in various contexts. Understanding this concept helps in making sense of financial decisions, statistical data interpretation, and everyday calculations.