# A complicated problem

• August 19th 2009, 03:11 PM
mydisguise08
A complicated problem
If you take the number of rocks you have, and divide them up into two unequal numbers, then 1545 times the difference between the two numbers equals three times the difference between the squares of the two numbers. How many rocks do you have? :confused:
• August 19th 2009, 04:47 PM
Soroban
Hello, mydisguise08!

Quote:

If you take the number of rocks you have and divide them into two unequal numbers,
then 1545 times the difference between the two numbers
equals three times the difference between the squares of the two numbers.

How many rocks do you have?

Spoiler:

Let the rocks be divided into two groups: $x$ rocks and $y$ rocks, $x > y$.

We are told: . $1545(x-y) \:=\:3(x^2-y^2)$

. . Factor: . $1545(x-y) \;=\;3(x-y)(x+y)$

. . Divide by $3(x-y)\!:\quad \boxed{x + y \;=\;515}$