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When a number is decreased by $4\%$ , the result is $66$ . What is the original number to the nearest tenth?

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Find the total given a part and a percent

Full solution

Q. When a number is decreased by

4\%

, the result is

66

. What is the original number to the nearest tenth?

Understand the problem: Understand the problem. $\newline$ We need to find the original number before a $4\%$ decrease that results in $66$ . To do this, we can represent the original number as $x$ and set up the equation $x - 0.04x = 66$ , where $0.04x$ is the $4\%$ decrease of the original number $x$ .
Simplify the equation: Simplify the equation. $\newline$ Combine like terms to simplify the equation: $x(1 - 0.04) = 66$ , which simplifies to $0.96x = 66$ .
Solve for x: Solve for x. $\newline$ Divide both sides of the equation by $0.96$ to find the original number $x$ . $\newline$ $x = \frac{66}{0.96}$
Perform the division: Perform the division to find $x$ . $\newline$ $x \approx 68.75$
Round the result: Round the result to the nearest tenth. The original number rounded to the nearest tenth is $68.8$ .

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