Question

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

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