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Bao bought stock in a company two years ago that was worth
x dollars. During the first year that she owned the stock, it decreased by
39%. During the second year the value of the stock decreased by
38%. Write an expression in terms of
x that represents the value of the stock after the two years have passed.
Answer:

Bao bought stock in a company two years ago that was worth $x$ dollars. During the first year that she owned the stock, it decreased by $39 \%$ . During the second year the value of the stock decreased by $38 \%$ . Write an expression in terms of $x$ that represents the value of the stock after the two years have passed. $\newline$ Answer:

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Evaluate two-variable equations: word problems

Full solution

Q. Bao bought stock in a company two years ago that was worth

x

dollars. During the first year that she owned the stock, it decreased by

39 \%

. During the second year the value of the stock decreased by

38 \%

. Write an expression in terms of

x

that represents the value of the stock after the two years have passed.

\newline

Answer:

Calculate Decreased Value: Determine the value of the stock after the first year. $\newline$ The stock decreased by $39\%$ in the first year. To find the decreased value, we calculate $39\%$ of $x$ and subtract it from $x$ . $\newline$ Decrease in value = $39\%$ of $x$ = $0.39 \times x$ $\newline$ Value after first year = $x - 0.39 \times x$ $\newline$ Simplify the expression to find the value after the first year. $\newline$ Value after first year = $x \times (1 - 0.39) = x \times 0.61$
Find Value After First Year: Determine the value of the stock after the second year. $\newline$ The stock decreased by $38\%$ in the second year. We need to apply this decrease to the value of the stock at the end of the first year. $\newline$ Decrease in value during second year = $38\%$ of the value after first year = $0.38 \times (x \times 0.61)$ $\newline$ Value after second year = Value after first year - Decrease during second year $\newline$ Value after second year = $x \times 0.61 - 0.38 \times (x \times 0.61)$ $\newline$ Simplify the expression to find the value after the second year. $\newline$ Value after second year = $x \times 0.61 \times (1 - 0.38) = x \times 0.61 \times 0.62$
Apply Decrease for Second Year: Write the final expression. $\newline$ The final expression that represents the value of the stock after two years is: $\newline$ Value after two years = $x \times 0.61 \times 0.62$

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