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When a number is decreased by
1.3%, the result is 45 . What is the original number to the nearest tenth?
Answer:

When a number is decreased by $1.3 \%$ , the result is $45$ . What is the original number to the nearest tenth? $\newline$ Answer:

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Find the total given a part and a percent

Full solution

Q. When a number is decreased by

1.3 \%

, the result is

45

. What is the original number to the nearest tenth?

\newline

Answer:

Understand the problem: Understand the problem. $\newline$ We need to find the original number before a decrease of $1.3\%$ resulted in $45$ . To do this, we can represent the original number as $100\%$ and the decrease as $1.3\%$ , which means the resulting number, $45$ , is $98.7\%$ of the original number.
Set up the equation: Set up the equation. $\newline$ Let the original number be $x$ . Then, $98.7\%$ of $x$ is equal to $45$ . $\newline$ So, we can write the equation as: $\newline$ $98.7\%$ of $x = 45$
Convert to decimal: Convert the percentage to a decimal and write the equation. $\newline$ $98.7\%$ as a decimal is $0.987$ . So the equation becomes: $\newline$ $0.987 \times x = 45$
Solve for x: Solve for x. $\newline$ To find $x$ , we divide both sides of the equation by $0.987$ : $\newline$ $x = \frac{45}{0.987}$
Perform division: Perform the division to find the original number. $x \approx 45.59$
Round the result: Round the result to the nearest tenth. The original number rounded to the nearest tenth is $45.6$ .

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