Converting word problem into algebra

Question

A microprocessor plant that manufactures computer chips costs $\$400,000$ per day to operate. It costs $\$30$ to produce one chip which sell for $\$190$ dollars. How many chips does the plant have to make to break even on one day operation?

Let $X$ be the number of chips I need to make.

$400,000 = 190X-30X$ (but I'm not sure this is even right). I'll continue anyway, I'll check it later...

$400000 = 160X$

$X=2500\quad$ ?

$2500 * 190 = 475000$ (its wrong)

Can someone help me? I think that formula I have is very wrong and I can't figure out another one...

Answer 1

You seem to have the correct answer (definitely the correct method to solve this). Why do you think "2500 * 190 = 475000" means you are wrong? Remember that the number of chips also takes into account their manufacture cost.

Answer 2

Your method of checking the answer is incorrect. $2500\cdot 190=475000$ is the total gross income from producing 2500 chips, but the cost of producing those 2500 chips is not just 400000, but $400000+2500\cdot 30=475000$, since each of the 2500 chips costs \$30 to produce.