Step-by-step explanation:
Let's pick some easy numbers for illustration.
Let x equal our initial stock purchase, and, say it was $100.
x = $100
The problem says it's value dropped by 17.2%. If x = 100 is 100% of our stock value the 17.2% less is
[tex]x - 0.172x = 0.828x[/tex]
So now our stock is worth 0.828(100) = $82.80.
Now how much of an increase do we need to get back to $100.
[tex]100 - 82.80 = 17.20[/tex]
So our base is $82.80 because our stock price dropped, we want to know what percent increase is $17.20 of $82.80
[tex]17.20 \div 82.80 = 0.2077[/tex]
Or 20.77% increase to get back to original price.
To make this generic, since $100 is not supplied information, substitute x for 100 and 0.828x for the amount of money dropped.
x = original stock value
[tex]x - 0.828x [/tex]
Is the amount of value lost, and to be regained in the second part of the question.
To find out what portion the decrease is of the new value
[tex] \frac{(x - 0.828x)}{0.828x} = \frac{0.172x}{0.828x} = 0.2077 [/tex]
Or 20.77%
