200% of what number is 26?
The Correct Answer and Explanation is :
To find what number 200% corresponds to when it equals 26, we can set up the equation based on the definition of percentage.
Explanation:
Step 1: Understanding Percentages
The term “percent” means “per hundred.” Therefore, when we say “200% of a number,” we are effectively saying “200 out of 100 times that number.” Mathematically, this can be represented as:
[
200\% = \frac{200}{100} = 2
]
This means that 200% of a number is simply twice that number.
Step 2: Setting Up the Equation
Let’s denote the unknown number as ( x ). According to the problem, we need to find ( x ) such that:
[
200\% \text{ of } x = 26
]
In mathematical terms, this can be expressed as:
[
2x = 26
]
Step 3: Solving for ( x )
To solve for ( x ), we divide both sides of the equation by 2:
[
x = \frac{26}{2}
]
Calculating this gives:
[
x = 13
]
Step 4: Conclusion
Therefore, the number we are looking for is 13.
Verification:
To verify our answer, we can check if 200% of 13 equals 26:
[
200\% \text{ of } 13 = 2 \times 13 = 26
]
This confirms that our solution is correct.
Summary
In summary, to find what number 200% corresponds to when it equals 26, we set up the equation ( 2x = 26 ) and solved for ( x ), resulting in ( x = 13 ). Understanding how to manipulate percentages is crucial for solving similar problems in mathematics, allowing us to relate various quantities effectively.