A man buys some bottle for $ \text{300} $ and when offloading he breaks $10$. He sells the remaining with a mark up of $4$ and makes $100$ profit on the entire transaction. How many bottles did he buy?
I know the cost of the bottle is $300/x$ but the problem I'm having is the equation will be more complex as he would need to cover up for the broken bottles. I know the answer is $50$ just don't know how to get there.
On
Let x be number of bottles.
Price of one bottle $\frac {300}{x}$
Selling price is $\frac {400}{x-10}$
Difference in price of 1 bottle is 4. So we have,
$\frac {400}{x-10} - \frac {300}{x} = 4$
$400x - 300(x-10) = 4x(x-10)$
$400x - 300x + 3000 = 4x^2 - 40x$
$100x + 3000 = 4x^2 - 40x$
$4x^2 - 40x -100x -3000 = 0$
$4x^2 - 140x - 3000 = 0$
$x^2 - 35x - 750 = 0$
$x^2 - 50x + 15x -750 = 0$
$x(x - 50) + 15(x - 50) = 0$
$(x - 50) (x + 15) = 0$
Rejecting $(x + 15)$ as it gives negative value.
$ (x - 50) = 0$
$x = 50$
x = no. of bottles brought
x - 10 = no. of bottles can be sold
marked up price of each bottle to be sold = $ (\dfrac {300}{x} + 4)$
$(x -10) (\dfrac {300}{x} + 4) - 300 = 100$