shares and stocks

Question

a company plans to issue 24500 shares of two different kinds of stock which will have combined value of $800000. one of the stocks is worth $100 per share and the other stock is worth $25 per share. how many shares of each stock will be issued

Answer 1

Let x=stock "A" and y= stock "B"

 

together they total 24500 stocks so:

x+y=24500

 

The cost of each stock is represented by 100(x) and 25(y) respectively

And the total cost of stocks sold is 800000, so:

 

100x+25y=800000

 

Rearrange the first equation and substitute it into the second equation to find the number of one of the stocks.

x=24500-y

 

100(24500-y)+25y=800000 Solve for y

2450000-100y+25y=800000

2450000-75y=800000

-75y=-1650000

y=22000

 

Remember y represents the number of stock "B" sold so if you know y you can put it into the original first equation and find x, or the number of stock "A" sold, so:

 

x+22000=24500

x=2500

 

The shares of one of the stocks sold is 22000 and the shares of the other stock sold is 2500

Put those numbers back into the equations to check your work