# 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. [[snippet]] 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. [[snippet]]
Incorrect. [[snippet]]
Correct. [[snippet]] __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. [[snippet]]
62%
71%
76%
85%
105%