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When a number is decreased by
5%, the result is 50 . What is the original number to the nearest tenth?
Answer:

When a number is decreased by $5 \%$ , the result is $50$ . What is the original number to the nearest tenth? $\newline$ Answer:

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Exponential growth and decay: word problems

Full solution

Q. When a number is decreased by

5 \%

, the result is

50

. What is the original number to the nearest tenth?

\newline

Answer:

Calculate Percentage: Determine the percentage of the original number that results in $50$ after a $5\%$ decrease. $\newline$ Since a $5\%$ decrease leaves us with $95\%$ of the original number, we can represent the original number as $100\%$ .
Set Up Equation: Set up the equation to find the original number. $\newline$ Let the original number be represented by $x$ . Then, $95\%$ of $x$ is equal to $50$ . $\newline$ So, the equation is $0.95x = 50$ .
Solve for Original Number: Solve the equation for $x$ to find the original number. $\newline$ Divide both sides of the equation by $0.95$ to isolate $x$ . $\newline$ $x = \frac{50}{0.95}$
Calculate Value of x: Calculate the value of $x$ . $x = \frac{50}{0.95}$ $x \approx 52.63157894736842$
Round to Nearest Tenth: Round the original number to the nearest tenth. $\newline$ The original number rounded to the nearest tenth is approximately $52.6$ .

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