michael purchased a certain number of shares of one stock for a total of $1400. The second stock was selling for 6$ less per share. Michael could have brought 3 more shares of the second stock for the same amount of money. How many shares of the first stick did michael purchase? How much did each share cost ?
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To solve this problem, let's assign variables to the unknowns:
Let x be the number of shares of the first stock that Michael purchased.
Let y be the cost per share of the first stock.
From the given information, we know that Michael spent a total of $1400 to purchase the shares of the first stock. Thus, we can set up the equation:
x * y = 1400 (equation 1)
We are also told that the second stock was selling for $6 less per share. This means the cost per share of the second stock would be (y - 6). Additionally, we know that Michael could have bought 3 more shares of the second stock for the same amount of money, which is $1400. We can set up another equation using this information:
(x + 3) * (y - 6) = 1400 (equation 2)
Now, we have a system of two equations with two unknowns. We can solve this system using substitution or elimination method. Let's use substitution method:
From equation 1, we have y = 1400 / x.
Now substitute this value of y in equation 2:
(x + 3) * (1400 / x - 6) = 1400
Simplify the equation:
(x + 3) * (1400 - 6x) = 1400
Expand and simplify:
1400x - 6x^2 + 4200 - 18x = 1400
Rearrange to get a quadratic equation:
-6x^2 + 1382x + 2800 = 0
Now, we can solve this quadratic equation. By factoring or using the quadratic formula, we find that x = 29 or x ≈ -15. Therefore, the number of shares of the first stock that Michael purchased is 29.
To find the cost per share, substitute this value of x into equation 1:
29 * y = 1400
Solve for y:
y ≈ $48.28
Therefore, Michael purchased 29 shares of the first stock and each share cost approximately $48.28.