Find the number is 900% of it is 450.
The Correct Answer and Explanation is :
To find the number where 900% of it equals 450, follow these steps:
Step 1: Understand the problem
The problem states that 900% of a number is 450. This can be written mathematically as:
[
900\% \times x = 450
]
Here, (x) represents the unknown number we need to find.
Step 2: Convert percentage to decimal
To work with percentages in equations, convert the percentage to a decimal.
- 900% can be written as:
[
900\% = \frac{900}{100} = 9
]
So the equation becomes:
[
9 \times x = 450
]
Step 3: Solve for (x)
To isolate (x), divide both sides of the equation by 9:
[
x = \frac{450}{9}
]
Step 4: Perform the division
Now, divide 450 by 9:
[
x = 50
]
So, the number is 50.
Explanation:
The key to solving percentage-based problems like this one is understanding how percentages represent parts of a whole. A percentage tells you how many parts per 100 of something. Here, 900% means 900 parts per 100, or 9 times the value of the number. We translated the percentage into its decimal form (9), then used algebra to solve for the unknown number (x).
Thus, when 900% of 50 is calculated:
[
9 \times 50 = 450
]
This confirms that the number is indeed 50.
This approach works for any percentage-based problem where you are given a percentage of an unknown number. By converting the percentage to a decimal and setting up a simple equation, you can solve for the unknown value.