Michael purchased a certain number of share of one stock for a total of $308. The second stock was selling for $3 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?
s shares at price p gives
sp = 308
(s+6)(p-3) = 308
sp+6p-3s-18 = 308
308+6p-3s = 18
2p-s = 6
2p - 308/p = 6
2p^2 - 6p - 308 = 0
p^2 - 3p - 154 = 0
(p-14)(p+11)
p = 14
s = 77
To solve this problem, let's first assume that Michael purchased x shares of the first stock.
The total cost of the first stock is $308. Therefore, the cost per share of the first stock is given by:
Cost per share of first stock = Total cost of first stock / Number of shares of first stock
= $308 / x
According to the given information, the second stock was selling for $3 less per share. Therefore, the cost per share of the second stock is given by:
Cost per share of second stock = Cost per share of first stock - $3
= ($308 / x) - $3
Michael could have bought 6 more shares of the second stock for the same amount of money. This means that the total cost of the second stock is the same as the total cost of the first stock. So, the total cost of the second stock is $308.
Total cost of second stock = Cost per share of second stock * Number of shares of second stock
= [($308 / x) - $3] * (x + 6)
Now, since the total cost of the second stock is given as $308, we can set up the equation:
$308 = [($308 / x) - $3] * (x + 6)
To solve this equation, we can simplify it as follows:
$308 = [($308 - 3x) / x] * (x + 6) // Simplified the expression inside the parentheses
$308 = (308 - 3x) / x * (x + 6) // Expanded the expression inside the brackets
$308 = (308 - 3x) * (x + 6) / x // Rewrote the equation
$308x = (308 - 3x) * (x + 6) // Multiplied both sides of the equation by x to remove the denominator
Now, we can simplify and solve this equation to find the value of x, which represents the number of shares of the first stock that Michael purchased.