SOLUTION: I purchased 300 shares; I purchased 3 times as many shares of common as I did preferred. Common shares currently have a par of $40, preferred shares cost 3/4 more. What is the per

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: I purchased 300 shares; I purchased 3 times as many shares of common as I did preferred. Common shares currently have a par of $40, preferred shares cost 3/4 more. What is the per       Log On


   

Question 325321: I purchased 300 shares; I purchased 3 times as many shares of common as I did preferred. Common shares currently have a par of $40, preferred shares cost 3/4 more. What is the per share price of preferred shares? And How much is my total purchase price of all shares?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
total shares is 300
x = common
y = preferred

purchased 3 times as many common as preferred so:

x = 3*y

common have a par of $40.
preferred cost 3/4 more.

preferred must cost 1.75 * common which makes the price of the preferred share equal to 70.

40 + 30 = 70

preferred is 3/4 more per share than the price of the common.

3/4 * 40 = 30.

total purchase price would be calculated as follows:

x + y = 300
x = 3*y making this equation:

3*y + y = 300 which becomes:
4*y = 300

divide both sides of the equation by 4 to get:

y = 75

since x = 3*y, then x = 225.

x + y = 300 results in 225 + 75 = 300 which is correct.

total purchase price of all shares is 225 * 40 + 75 * 70 = 14250