A magician is training for an underwater escape trick. Using a new technique, she can hold her breath for $57$ seconds. That is $50\%$ more than she was able to do when she first tried. How long could the magician hold her breath when she first tried? $\newline$ ____ seconds

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Q. A magician is training for an underwater escape trick. Using a new technique, she can hold her breath for

57

seconds. That is

50\%

more than she was able to do when she first tried. How long could the magician hold her breath when she first tried?

\newline

____ seconds

Define current time: Define the current breath-holding time and the percentage increase. $\newline$ Current time = $57$ seconds, which is $50\%$ more than the initial time. $\newline$ Let $x$ be the initial time. $\newline$ Expression for current time: $x + 50\%(x) = x + 0.5x$ .
Set up equation: Set up the equation based on the information given. $\newline$ $57 = x + 0.5x$ $\newline$ Combine like terms: $1.5x = 57$ .
Solve for x: Solve for x, the initial breath-holding time. $\newline$ $1.5x = 57$ $\newline$ $x = \frac{57}{1.5}$ $\newline$ $x = 38$ seconds.