Question

An investor bought 300 shares of stock, some at $3.25 per share and some at $5.50 $ per share. If the total cost was $1312.50 $ how many shares of each stock did the investor buy? (Round to two decimal places if necessary.)

Answer 1

Step-by-step explanation

Let the number of stocks the investor bought at $3.25 per share be x and those she bought for $5.50 $ per share be y. Therefore;

`x+y=300`

Also, since the investor spent a total of $1312.50. Therefore;

`3.25x+5.50y=1312.50`

Therefore, we will isolate for x in equation 1

`x=300-y`

Substitute the above in equation 2

`\begin{gathered} \begin{bmatrix}3.25\left(300-y\right)+5.5y=1312.5\end{bmatrix} \\ \begin{bmatrix}975+2.25y=1312.5\end{bmatrix} \\ 2.25y=1312.5-975 \\ 2.25y=337.5 \\ y=(337.5)/(2.25) \\ y=150 \end{gathered}`

Therefore;

`x=300-y\Rightarrow x=300-150=150`

Answer: He bought 150 shares for each stock