michael purchased a certain number of one stock for a total of $176. the second stock was selling for $5 less per share. michael could have bough 5 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?
If he purchased x shares for price p, then
xp = 176
But,
(x+5)(p-5) = xp
xp + 5p - 5x - 25 = xp
p-x-5 = 0
but, p = 176/x, so
176/x - x - 5 = 0
x = 11
11*16 = 176
16*11 = 176
The answer is michael bought 11 shares each costing $16
To solve this problem, let's assume that Michael purchased x shares of the first stock.
According to the given information, the total cost of the first stock is $176. Therefore, the cost of each share of the first stock can be calculated by dividing the total cost by the number of shares:
Cost per share of the first stock = Total cost of the first stock / Number of shares of the first stock
= $176 / x
Now, we know that the second stock was selling for $5 less per share. So, the cost per share of the second stock would be:
Cost per share of the second stock = Cost per share of the first stock - $5
= $176 / x - $5
It is also mentioned that Michael could have bought 5 more shares of the second stock for the same amount of money. This implies that the cost of the second stock should remain the same, even with 5 more shares.
Therefore, we can set up an equation using the above information:
Total cost of the second stock = (Cost per share of the second stock) * (Number of shares of the second stock)
= ( $176 / x - $5 ) * (x + 5)
Since the total cost of the second stock should be equal to the total cost of the first stock, we can equate the two expressions:
$176 = ( $176 / x - $5 ) * (x + 5)
Now, we can solve this equation to find the value of x, which represents the number of shares of the first stock that Michael purchased.