Question

An investor bought 300 shares of stock, some at $8.00 per share and some at $5.75 per share. If the total cost was $2006.25, how many shares of each stock did the investor buy?

Answer 1

Step 1: construct equations

• Let Xbe number of shares at $8.00

• Let Y be number of shares at $5.75

,

• Then, X +Y = 300 .....(equation 1 ); therefore ,x = 300-y

,

• And, 8.00x + 5.75y = 2006.25 .......(equation 2)

Step 2: Subsitute the value of x into equation 2 , and solve for y

8.00( 300-y) + 5.75y = 2006.25

2400 -8y +5.75y = 2006.25

-2.25y = 2006.25-2400

-2.25y = -393.75

Therefore, y = (-393.75/-2.25) = 175

Step 3 : Substitude the value of y = 175 into equation 1 , solve for x

X +Y = 300

x = 300 -175 = 125

Therefore, X = 125

This means that an investor bought 125 stock at $8.00 and also bought 175 stock at $5,75 .