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

Algebra ->  Expressions-with-variables -> 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      Log On


   

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) About Me  (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 +n+%2B+1+ = the number of horses he bought
+n+ = the number of horses he sold
-----------------
The price he paid for each horse was:
+900+%2F+%28+n+%2B+1+%29+
------------------
The amount he received for each horse when he sold them was:
+1800+%2F+n+
------------------
His profit for each horse was:
+1800%2Fn+-+900%2F%28+n%2B1+%29+=+110+
Multiply both sides by +n%2A%28+n%2B1+%29+
+1800%2A%28+n%2B1+%29+-+900n+=+110%2An%2A%28+n%2B1+%29+
+1800n+%2B+1800++-+900n+=+110n%5E2+%2B+110n+
+110n%5E2+-+790n+-+1800+=+0+
+11n%5E2+-+79n+-+180+=+0+
Use the quadratic formula
+n+=+%28+-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+11+
+b+=+-79+
+c+=+-180+

+n+=+%28+79+%2B-+sqrt%28+6241+%2B+7920+%29%29+%2F+22+
+n+=+%28+79+%2B-+sqrt%28+14161+%29%29+%2F+22+
+n+=+%28+79+%2B+119+%29+%2F+22+
+n+=+198%2F22+
+n+=+9+
+n+%2B+1+=10+
He bought 10 horses
check:
+1800%2Fn+-+900%2F%28+n%2B1+%29+=+110+
+1800%2F9+-+900%2F%28+9%2B1+%29+=+110+
+200+-+90+=+110+
+110+=+110+
OK

Answer by TimothyLamb(4379) About Me  (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
---
Free algebra tutoring live chat:
https://sooeet.com/chat.php?gn=algebra
---
Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations with quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
---
Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
---