An investor has an account with stock from two different companies. Last year, her stock in Company A was worth $\$ 3180$ and her stock in Company B was worth $\$ 940$ . The stock in Company A has increased $20\%$ since last year and the stock in Company $B$ has increased $15 \%$ . What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth (if necessary). $\newline$ Answer:

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Grade 8

Percent of change: word problems

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Q. An investor has an account with stock from two different companies. Last year, her stock in Company A was worth

\$ 3180

and her stock in Company B was worth

\$ 940

. The stock in Company A has increased

20\%

since last year and the stock in Company

B

has increased

15 \%

. What was the total percentage increase in the investor's stock account? Round your answer to the nearest tenth (if necessary).

\newline

Answer:

Calculate Stock Value Increase: Calculate the new value of the investor's stock in Company A after a $20$ % increase. $\newline$ Original value of stock in Company A: $\$3180$ $\newline$ Percentage increase: $20\%$ $\newline$ New value = Original value + (Percentage increase $\times$ Original value) $\newline$ New value = $\$3180 + (0.20 \times \$3180)$ $\newline$ New value = $\$3180 + \$636$ $\newline$ New value = $\$3816$
Calculate Total Stock Value Last Year: Calculate the new value of the investor's stock in Company B after a $15$ % increase. $\newline$ Original value of stock in Company B: $\$940$ $\newline$ Percentage increase: $15\%$ $\newline$ New value = Original value + (Percentage increase $\times$ Original value) $\newline$ New value = $\$940$ + $(0.15 \times \$940)$ $\newline$ New value = $\$940$ + $\$141$ $\newline$ New value = $\$1081$
Calculate Total Stock Value This Year: Calculate the total value of the investor's stock last year. $\newline$ Total value last year = Value of stock in Company A + Value of stock in Company B $\newline$ Total value last year = $\$3180$ + $\$940$ $\newline$ Total value last year = $\$4120$
Calculate Total Increase: Calculate the total value of the investor's stock this year. $\newline$ Total value this year = New value of stock in Company A + New value of stock in Company B $\newline$ Total value this year = $\$3816$ + $\$1081$ $\newline$ Total value this year = $\$4897$
Calculate Total Percentage Increase: Calculate the total increase in the investor's stock account. $\newline$ Total increase = Total value this year - Total value last year $\newline$ Total increase = $\$4897$ - $\$4120$ $\newline$ Total increase = $\$777$
Calculate Total Percentage Increase: Calculate the total increase in the investor's stock account. $\newline$ Total increase = Total value this year - Total value last year $\newline$ Total increase = $\$4897 - \$4120$ $\newline$ Total increase = $\$777$ Calculate the total percentage increase in the investor's stock account. $\newline$ Total percentage increase = (Total increase / Total value last year) $\times$ $100$ \% $\newline$ Total percentage increase = ( $\$777 / \$4120$ ) $\times$ $100$ \% $\newline$ Total percentage increase = $0.1885 \times 100\%$ $\newline$ Total percentage increase = $18$ . $85$ \% $\newline$ Round to the nearest tenth: $18.9\%$