Question

An investor bought 400

shares of stock, some at $1.75
per share and some at $3.25
per share. If the total cost was $1112.50
, how many shares of each stock did the investor buy? (Round to two decimal places if necessary.)

Answer 1

Let x be the number of shares bought at $1.75 per share and y be the number of shares bought at $3.25 per share. Then we have the following system of equations:

x + y = 400 (the total number of shares is 400)

1.75x + 3.25y = 1112.50 (the total cost of the shares is $1112.50)

We can solve for x by rearranging the first equation:

x = 400 - y

Substituting this into the second equation, we get:

1.75(400 - y) + 3.25y = 1112.50

Expanding and simplifying, we get:

700 - 1.75y + 3.25y = 1112.50

1.5y = 412.50

y = 275

Substituting this value of y back into the equation x + y = 400, we get:

x + 275 = 400

x = 125

Therefore, the investor bought 125 shares at $1.75 per share and 275 shares at $3.25 per share.