# Video: Systems of Equations

A cellphone factory produces 𝑥 cellphones with cost 𝐶(𝑥) = 150𝑥 + 10000 and revenue 𝑅(𝑥) = 200𝑥. What is the breakeven point?

02:14

### Video Transcript

A cellphone factory produces 𝑥 cellphones with cost 𝐶 of 𝑥 equals 150𝑥 plus 10000 and revenue 𝑅 of 𝑥 equals 200𝑥. What is the break-even point?

Well, if we look at what the words mean in this question, we’ve got revenue. Well, revenue is the money taken. So, it’s the money taken by the factory. Then, we next got another word which might be unfamiliar to you, and that is breakeven or the break-even point. This is the point where the cost and the revenue are the same. So, the amount the company has paid out and the amount that the company is taking in are equal. And because of this relationship, what we can do is set our two equations equal to each other.

So, we can say that 150𝑥 plus 10000 is equal to 200𝑥. And we can do that because that’s means that if we find out what 𝑥 is, then we can work out how many phones the factory will need to sell in order to break even because 𝑥 is the number of phones. So, to solve the equation, the first thing we do is subtract 150𝑥 from both sides. When we do that, we get 10000 is equal to 50𝑥. And then, in order to work out what 𝑥 is, we divide both sides of the equation by 50. So, we get that 200 is equal to 𝑥.

And if we think about how we could work that out, well, if we have 10000 over 50, well then the first thing we can do is divide both the numerator and denominator by 10. So, we’re gonna knock off a zero. So then, we’ve got 1000 divided by five. And therefore, if we’ve got 1000 divided by five, we can think of it as fives into 10 goes twice. And then, we’ve got two zeros left, so that’s gonna be 200. So therefore, we can say that 1000 divided by five will be 200. So therefore, 10000 divided by 50 will be 200. So therefore, we can say that the break-even point is gonna be when 𝑥 is equal to 200. So, what this means is the break-even point will be when the factory sells 200 cellphones.