Margaret wants to buy 200 shares of stock in an Internet...

Margaret wants to buy 200 shares of stock in an Internet company. She buys some shares at $\$ 8.125$ per share and the rest when the price has gone up to $\$ 9.375$ per share. If she spent a total of $\$ 1,725$ for all the shares, how many shares did she buy at each price?

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Key Concepts

System of Linear Equations

A system of linear equations is a set of equations with multiple variables that are solved together because they share common unknowns. In the context of this problem, one equation represents the total number of shares purchased, while another represents the total cost of those shares. This system allows for determining how many shares are bought at each price by satisfying both conditions simultaneously.

Substitution Method

The substitution method is a common technique used to solve systems of equations, where one solves one of the equations for a variable and then substitutes that expression into the other equation. This reduces the system to a single equation with one unknown, making it easier to find the solution. It is particularly useful when the equations are set up to express one variable in terms of another.

Weighted Average in Investment

The weighted average in an investment context involves combining different quantities that are bought at various prices to calculate an overall average cost. Each price is multiplied by the number of shares purchased at that price, and the sum of these products is divided by the total number of shares. This concept shows how varying unit costs impact the overall spending and is essential in solving problems where quantities are purchased at different prices.

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