Percents: Percent Translation
Steven and Brandon both invested the same amount into different stock portfolios. Steven's portfolio lost 40% of its value in the first year and gained 25% in the second year. If Brandon's portfolio gained 40% of its value in the first year and lost 25% in the second year, after two years, Steven's stocks are worth approximately what percent of Brandon's stocks?
Incorrect.
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Steven's losses were greater and his gains were less than Brandon's, so his stocks will be worth less, not more, than Brandon's.
Incorrect.
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Incorrect.
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Correct.
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__Plug In__ 100 for Steven's and Brandon's investments (the invisible variable). If Steven invests $100, a loss of 40% would leave him with $$ $100-$40=$60$$ after the first year, and after a gain of 25% in the second year, Steven will have $$ $60+$15=$75$$.
If Brandon invests $100, a gain of 40% would give him $$ $100+$40=$140$$ after the first year, and after a loss of 25% in the second year, Brandon will have $$ $140-$35=$105$$. Now translate the question:
{color:purple}Steven's stocks are worth approximately what percent of Brandon's stocks?{/color}
>$$\displaystyle 75=\frac{x}{100}\cdot105$$
>$$\displaystyle \frac{75}{105}= \frac{x}{100}$$
By ballparking, $$\frac{75}{105} \approx \frac{70}{100} = 0.7$$ and therefore
>$$\displaystyle x \approx 0.7\cdot 100 = 70$$
Thus, Steven's stocks must be worth approximately 71% of Brandon's.
Incorrect.
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62%
71%
76%
85%
105%
