SOLUTION: A man bought a number of horses for $900. After training them, he sold all but one to a dude ranch owner at a profit of $110 each, thereby realizing a profit of 100% on the whole t

Question 936063: A man bought a number of horses for $900. After training them, he sold all but one to a dude ranch owner at a profit of $110 each, thereby realizing a profit of 100% on the whole transaction. How many horses did he buy?
Found 2 solutions by josmiceli, TimothyLamb:
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
He bought the horses for $900 and made a profit of
100%, so he sold the horses for $1800
----------------
Let = the number of horses he bought
= the number of horses he sold
-----------------
The price he paid for each horse was:

------------------
The amount he received for each horse when he sold them was:

------------------
His profit for each horse was:

Multiply both sides by

Use the quadratic formula

He bought 10 horses
check:

OK

Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
x = number of horses purchased
---
y = cost per horse:
y = 900/x
---
z = sale price per horse:
z = 110 + y
---
w = total revenue from sale:
w = (x - 1)z
---
(w - 900)/900 * 100 = 100
(w - 900)/900 = 100/100
w - 900 = 900
w = 1800
---
w = 1800
(x - 1)z = 1800
(x - 1)(110 + y) = 1800
110x + xy - 110 - y = 1800
110x + x900/x - 110 - 900/x = 1800
110x + 900 - 110 - 900/x = 1800
110x + 900 - 110 - 1800 = 900/x
110x - 1010 = 900/x
110xx - 1010x - 900 = 0
---
the above quadratic equation is in standard form, with a=110, b=-1010 and c=-900
---
to solve the quadratic equation, by using the quadratic formula, copy and paste this:
110 -1010 -900
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
---
the quadratic has two real roots at:
---
x = 10
x = -0.818181818
---
the negative root doesn't fit the problem statement, so use the positive root:
---
answer:
x = number of horses purchased = 10
---
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