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Ella bought stock in a company two years ago that was worth
x dollars. During the first year that she owned the stock, it increased by
16%. During the second year the value of the stock increased by
40%. Write an expression in terms of
x that represents the value of the stock after the two years have passed.
Answer:

Ella bought stock in a company two years ago that was worth $x$ dollars. During the first year that she owned the stock, it increased by $16 \%$ . During the second year the value of the stock increased by $40 \%$ . 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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Add and subtract integers: word problems

Full solution

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

x

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

16 \%

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

40 \%

. Write an expression in terms of

x

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

\newline

Answer:

Calculate Increase in First Year: Let's start by calculating the increase in the stock's value during the first year. An increase of $16\%$ on the original value $x$ can be calculated by multiplying $x$ by $16\%$ or $0.16$ . $\newline$ Calculation: $x \times 0.16 = 0.16x$
Find Total Value After First Year: Now, let's add this increase to the original value to find the total value of the stock after the first year. $\newline$ Calculation: $x + 0.16x = 1x + 0.16x = 1.16x$
Calculate Increase in Second Year: For the second year, the stock increases by $40$ %. To find the new value, we need to multiply the value at the end of the first year $1.16x$ by $40$ % or $0.40$ . $\newline$ Calculation: $1.16x \times 0.40 = 0.464x$
Find Total Value After Two Years: We add this second year's increase to the value of the stock at the end of the first year to find the total value of the stock after two years. $\newline$ Calculation: $1.16x + 0.464x = 1.16x + 0.40(1.16x) = 1.16x(1 + 0.40) = 1.16x \times 1.40$
Simplify Final Expression: Now, let's simplify the expression to find the final expression that represents the value of the stock after two years. $\newline$ Calculation: $1.16x \times 1.40 = 1.624x$

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