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Sophie 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
34%. During the second year the value of the stock increased by
24%. Write an expression in terms of
x that represents the value of the stock after the two years have passed.
Answer:

Sophie 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 $34 \%$ . During the second year the value of the stock increased by $24 \%$ . 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. Sophie 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

34 \%

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

24 \%

. Write an expression in terms of

x

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

\newline

Answer:

Calculate Decrease in Value: Sophie's initial investment is worth $x$ dollars. In the first year, the stock decreases by $34\%$ . To find the decreased value, we calculate $34\%$ of $x$ and subtract it from $x$ .
Decrease in value = $34\%$ of $x$ = $0.34 \times x$
Value after first year = $x - 0.34 \times x$
Simplify Value After $1$ st Year: Now, let's simplify the expression for the value after the first year. $\newline$ Value after first year = $x - 0.34 \times x = (1 - 0.34) \times x = 0.66 \times x$
Calculate Increase in Value: In the second year, the value of the stock increases by $24\%$ . To find the increased value, we calculate $24\%$ of the value after the first year and add it to the value after the first year. $\newline$ Increase in value = $24\%$ of $0.66 \times x = 0.24 \times 0.66 \times x$ $\newline$ Value after second year = $0.66 \times x + 0.24 \times 0.66 \times x$
Simplify Value After $2$ nd Year: Now, let's simplify the expression for the value after the second year. $\newline$ Value after second year = $0.66 \times x + 0.24 \times 0.66 \times x = (1 + 0.24) \times 0.66 \times x = 1.24 \times 0.66 \times x$
Find Final Stock Value: Finally, we simplify the expression to find the final value of the stock after two years. $\newline$ Value after two years = $1.24 \times 0.66 \times x = 0.8184 \times x$

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