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When a number is increased by
3.4%, the result is 85 . What is the original number to the nearest tenth?
Answer:

When a number is increased by $3.4 \%$ , the result is $85$ . 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 increased by

3.4 \%

, the result is

85

. 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 $3.4\%$ increase that results in $85$ . $\newline$ To do this, we can represent the original number as $x$ and set up the equation $x + 0.034x = 85$ , because a $3.4\%$ increase is the same as multiplying the original number by $1.034$ .
Set up the equation: Set up the equation. $\newline$ Let $x$ be the original number. Then, the equation to represent the situation is: $\newline$ $x + 0.034x = 85$ $\newline$ This simplifies to: $\newline$ $1.034x = 85$
Solve for x: Solve for x. $\newline$ To find x, we need to divide both sides of the equation by $1.034$ : $\newline$ $x = \frac{85}{1.034}$
Perform the division: Perform the division to find the original number. $\newline$ $x = \frac{85}{1.034}$ $\newline$ $x \approx 82.2085$
Round the result: Round the result to the nearest tenth. $\newline$ The original number rounded to the nearest tenth is approximately $82.2$ .

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