Chapter 5.2, Problem 26E

To determine

To find:The shares of each stock the investor owns.

Answer to Problem 26E

The required answer is the total shares the investor own from Stock A is 80 and from Stock B is 120.

Explanation of Solution

Given information:

An investor owns shares of Stock A and Stock B. The investor owns a total of 200 shares with a total value of $4000.

  

Calculation:

Total shares $=200$

Total value $=\$4000$

Let shares of stock A be $x$

And shares of stock B be $y$

Therefore,

  $\begin{array}{l}\Rightarrow x+y=200\\ \Rightarrow x+y-y=200-y\end{array}$

(Subtract y from both sides)

  $\Rightarrow x=200-y$

(Equation 1)

Again,

  $\begin{array}{l}\Rightarrow x\cdot 9.5+y\cdot 27=4000\\ \Rightarrow 9.5\left(200-y\right)+27y=4000\end{array}$ (Putting the value of x)

  $\Rightarrow 1900-9.5y+27y=4000$

(Simplify)

  $\Rightarrow 1900-1900+17.5y=4000-1900$

(Subtract 1900 from both side)

  $\Rightarrow 17.5y=2100$

(Simplify)

  $\Rightarrow \frac{17.5y}{17.5}=\frac{2100}{17.5}$

(Divide by 17.5 on both sides)

  $\Rightarrow y=120$

(Simplify)

Therefore, from equation 1 we get:

  $\begin{array}{l}\Rightarrow x=200-y\\ \Rightarrow x=200-120\end{array}$

(Putting the value of y)

  $\Rightarrow x=80$

Therefore, the total shares the investor owns from stock A is 80 and from stock B is 120.