Question

Nora bought 100 shares of a technology stock and 200 shares of a mutual fund for 3200. Her sister, Erin bought 300 shares of technology and 50 shares of the same mutual fund for 5200. Find the cost per share of technology stock, and the cost per share of the mutual fund.

Answer 1

Cost per share of technology stock: $16.00

Cost per share of the mutual fund: $8.00

Step-by-step explanation:

Let be "t" the cost per share (in dollars) of technology stock and "m" the cost per share (in dollars) of the mutual fund.

Set up a System of equations:

`\left \{ {{100t+200m=3200} \atop {300t+50m=5200}} \right.`

You can use the Elimination Method to solve the System of equations:

- You can multiply the first equation by -3, then add both equations and solve for "m":

`\left \{ {{-300t-600m=-9600} \atop {300t+50m=5200}} \right.\\..................................\\-550m=-4400\\\\m=(-4400)/(-550)\\\\m=8`

- Finally, substitute the value of "m" into any original equation and solve for "t" in order to find its value:

`100t+200(8)=3200\\\\100t=3200-1600\\\\t=(1600)/(100)\\\\t=16`