I need help I don't know how to begin the equation
Michael purchased a certain number of share of one stock for a total of $2800. The second stock was selling for $6 less per share . Michael could have bought 6 more shares of the second stock for the same amount of money. How many shares of the first stock did Michael purchase? How much did each share cost?
To find the number of shares of the first stock Michael purchased, as well as the cost per share, we can set up a system of equations.
Let's denote the number of shares of the first stock as "x" and the cost per share as "c".
Based on the given information, we know that Michael spent a total of $2800 on the first stock, so the equation representing this is:
x * c = 2800 ----- Equation 1
We are also told that the second stock was selling for $6 less per share than the first stock. Therefore, the cost per share of the second stock can be represented as "(c - 6)".
According to the given information, Michael could have bought 6 more shares of the second stock for the same amount of money as he spent on the first stock. This can be represented by the equation:
(x + 6) * (c - 6) = 2800 ----- Equation 2
Now we have a system of two equations with two variables (x and c). We can solve this system to find the values of x and c.
To do this, we'll use the method of substitution:
1. Solve Equation 1 for c:
c = 2800 / x
2. Substitute this value of c into Equation 2:
(x + 6) * (2800 / x - 6) = 2800
Now we have a single equation with only one variable (x). We can simplify and then solve for x.