What is the number if 40% of 40% of a number is 40?

Understand the Problem

The question asks to find a number such that 40% of 40% of it equals 40. This is a straightforward percentage problem that can be solved by setting up an equation and solving for the unknown number.

Answer

$250$

Steps to Solve

Convert percentages to decimals

Convert the percentages to decimals by dividing by 100. So, 40% becomes $40/100 = 0.40 = 0.4$.

Set up the equation

Let $x$ be the unknown number. The problem states that 40% of 40% of $x$ equals 40. This can be written as an equation:

$0.4 \times 0.4 \times x = 40$

Simplify the equation

Multiply the decimals:

$0.16x = 40$

Solve for $x$

Divide both sides of the equation by 0.16 to isolate $x$:

$x = \frac{40}{0.16}$

Calculate the value of $x$

$x = 250$

More Information

The number we are looking for is 250. 40% of 250 is 100, and 40% of 100 is 40.

Tips

A common mistake is misinterpreting the wording and calculating 40% of a number and then taking 40% of the result. It's crucial to set up the equation correctly by multiplying the percentages together with the unknown number. Another mistake is forgetting to convert the percentages into decimals or fractions before performing the calculations.

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