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?
Say he bought n shares for $x of 1st stock.
nx = 28000
(n+6)(x-6) = 28000
nx+6x-6n-36 = 28000
we know nx=28000, so
6x-6n = 36
x-n=6
now, n=28000/x, so
x - 28000/x = 6
x^2 - 6x - 28000 = 0
x = 3±√28009
x = 170.36
164.36*170.36 = 28000.37
170.36*164.36 = 28000.37
Odd that the solution was not integers
she bought 50 shares at the cost of 56. Yay
Let's assume that Michael purchased x shares of the first stock.
The total amount spent on the shares of the first stock can be calculated by multiplying the number of shares (x) by the cost per share of the first stock.
So, the cost of x shares of the first stock is x * (cost per share of the first stock).
We know that the total amount spent on the shares of the first stock is $2800. So, we have the equation:
x * (cost per share of the first stock) = $2800 ----- (Equation 1)
Now, let's consider the second stock.
The cost per share of the second stock is $6 less than the cost per share of the first stock. So, the cost per share of the second stock can be written as (cost per share of the first stock) - $6.
If Michael bought 6 more shares of the second stock for the same amount of money, then the total amount spent on the shares of the second stock can be calculated by multiplying the number of shares (x + 6) by the cost per share of the second stock.
So, the cost of (x + 6) shares of the second stock is (x + 6) * (cost per share of the second stock).
We know that the total amount spent on the shares of the second stock is also $2800. So, we have the equation:
(x + 6) * (cost per share of the second stock) = $2800 ----- (Equation 2)
We can now solve this system of equations to find the values of x (number of shares of the first stock) and (cost per share of the first stock).
From Equation 1, we have:
x * (cost per share of the first stock) = $2800
From Equation 2, we have:
(x + 6) * (cost per share of the second stock) = $2800
Now, substitute (cost per share of the second stock) with (cost per share of the first stock - $6) in Equation 2:
(x + 6) * ((cost per share of the first stock) - $6) = $2800
Expand and simplify this equation:
(x + 6) * (cost per share of the first stock) - 6 * (x + 6) = $2800
Now, we can substitute (cost per share of the first stock) with (2800 / x) in the above equation (using Equation 1):
x * (2800 / x) - 6 * (x + 6) = $2800
Simplify this equation:
2800 - 6x - 36 = $2800
Simplify further:
-6x - 36 = 0
Now, solve for x:
-6x = 36
Divide both sides by -6:
x = -6
Since the number of shares cannot be negative, let's ignore this solution.
Therefore, there is no valid value of x (number of shares of the first stock) that satisfies the given conditions.