40 is 160 percent of what number

40 is 160 percent of what number?

The Correct Answer and Explanation is :

To find out what number 40 is 160 percent of, you can set up the equation based on the definition of percentages. When you say that 40 is 160 percent of a number ( x ), it means:

[
40 = 1.6 \times x
]

To find ( x ), you can rearrange this equation:

[
x = \frac{40}{1.6}
]

Now, let’s calculate that:

[
x = \frac{40}{1.6} = 25
]

So, 40 is 160 percent of 25.

Explanation

Percentages are a way of expressing a number as a fraction of 100. In this context, “160 percent” means 160 out of 100, or 1.6 when expressed as a decimal. When you say that one number is a percentage of another, you are essentially stating that the first number is that fraction of the second number.

In this case, we have 40 as the first number, and we need to find the second number, which we will denote as ( x ). By setting up the equation, we can directly relate these two values using the concept of percentages. The equation ( 40 = 1.6 \times x ) indicates that 40 is equal to 1.6 times the number we are looking for.

To isolate ( x ), we divide both sides of the equation by 1.6. This calculation shows how many times 1.6 fits into 40, giving us the original number we are trying to find. The result is 25, which can be confirmed by reversing the operation: if you take 25 and multiply it by 1.6, you will indeed get 40.

This method illustrates a fundamental principle of working with percentages, making it a valuable skill in various mathematical and real-world applications, from finance to statistics.