Develop an equation and solve algebraically

Question

a farmer buys some horses.If he pays $900 for the horses and sells all but one for 100% profit and gets $110 profit on each horse sold, how many horses did he buy?

Answer 1

Assuming each horse costs the same, the price of each horse is 900/n

He sold each horse for $110 profit, meaning he sold the horses for 900/n + 110 each

(n-1) of these horses made a total profit of 100% which is $900, since 100% of $900 = $900.

So that means the total amount collected for all (n-1) horses is 1800.

(n-1) (900/n + 110) = 1800

900 + 110n - 900/n - 110 = 1800

790 + 110n - 900/n = 1800

110n - 900/n = 1010

110n^2 - 900 = 1010n

110n^2 - 1010n - 900 = 0

11n^2 - 101n - 90 = 0

(11n + 9)(n - 10) = 0

11n + 9 = 0 results in negative values

n-10 = 0 ---> n = 10 horses

the ORIGINAL price of each horse is then $900/10 = $90.

Since he sold each for $110 profit, he sold them for $200 each.

9 x $200 = $1800 which is $900 profit

the answer is 10 horses