Chapter 5.2, Problem 26E

To determine

To describe:the number ofshares owned by the investor

Answer to Problem 26E

Therefore, there are $\text{80}$ shares in stock $\text{A}$ and $\text{120}$ shares in stock $\text{B}$

Explanation of Solution

Given:

There are $200$ shares

Totalvalue of shares is $\$4000$ .

Stock	Price
$A$   $B$	$\$9.50$   $\$27.00$

Calculation:

  $26.$

Let:

  $x\to$ number of shares in stock $A$

  $y\to$ number of shares in stock $B$

Setup the equations.

The number of problem is $200$ :

  $x+y=200\leftarrow \text{Eq}\text{.1}$

The total value of the shares is $\$4000$ :

  $\$9.50+27y=4000\leftarrow \text{Eq}\text{.2}$

Solve for one variable in using eq. $\text{1}$ :

  $\text{y=200-x}$

Substitute on eq. $\text{2}$ :

  $9.5x+27\left(200-x\right)=4000$

Simplify & solve for $x$ :

  $\begin{array}{l}9.5x+27\left(200-x\right)=4000\\ 17.5x=1400\to \text{x=80}\end{array}$

Solve for $\text{y}$ :

  $y=200-80\to \text{y=120}$

Therefore, there are

  $\text{80}$ shares in stock $\text{A}$ &

  $\text{120}$ shares in stock $\text{B}$

Result

See answer above

Conclusion:

Therefore, there are $\text{80}$ shares in stock $\text{A}$ and $\text{120}$ shares in stock $\text{B}$