Question

5. Fifty shares of GHX and nineteen shares of SPS cost $121.99. If fifty shares ofGHX cost a penny more than the nineteen shares of SPS, how much is the shareprice of each stock?

Answer 1

Given:

The cost of 50 shares of GHX and 19 shares of SPS is $121.99.

Fifty shares of GHX cost a penny more than the nineteen shares of SPS.

The objective is to find the share price of each stock.

Step-by-step explanation:

Consider the shares of GHX as x and shares of SPS as y.

Then, the equation of total cost can be written as,

`50x+19y=121.99\text{ . . . . . (1)}`

Since 50 shares of x cost a penny more than 19 shares of y then the equation can be written as,

`\begin{gathered} 50x-19y=1\text{ penny} \\ 50x-19y=0.01\text{ dollar . . . . .(2)} \end{gathered}`

To find x :

On adding equation (1) and equation (2),

`\begin{gathered} (50x+19y)+(50x-19y)=121.99+0.01 \\ 100x=122 \\ x=(122)/(100) \\ x=1.22 \end{gathered}`

To find y :

Now, substitute the value of x in equation (1).

`\begin{gathered} 50(1.22)+19y=121.99 \\ 61+19y=121.99 \\ 19y=121.99-61 \\ y=(60.99)/(19) \\ y=3.21 \end{gathered}`

Hence, the price of GHS stock is $1.22, and the price of SPS stock is $3.21.