ʕ•ᴥ•ʔ System of Linear Equations: Word Problem with Money

Описание: Quickly master how to solve linear equations word problem with money. Watch more lessons like this and try our practice at
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Show me the money! In this lesson, we are going to solve some linear equations word problems that are related to money.

Hi, welcome to this question right here. Andy, actually that's the man right there, is paid on the base salary plus commission for selling furniture, right? So it's a pretty good job up there. So he's selling something, he not only got the base salary, also gets a little bit of commission. So what happens in one week, he sold $5,000 worth of furniture. But, he was only paid $550 bucks. So for the first equation, just by reading that first sentence right there, okay? For that week, what happened is, he was paid $550. So that's how much money he earned. But, we know that the money that he earns is only based on the commission, plus the base salary. So we don't know how much the commission is, so let's use C for that. But it was based on the $5,000 worth of furniture. So there's your $5,000 furniture, worth of the goods that he sold and plus the base salary. So we don't know the base salary, so let's put a B right there. So that's your first equation for the first sentence right there. And, another week later, I was paid $450 bucks. So, $450 bucks this time, because I only sold $3,500 worth of furniture. So here's my commission, which I don't know yet, but I know I sold this much of the furniture and I still don't know my base salary. So those are my two equations right over here: a, b, c, right here we have: what is the rate of commission? That is the commission C right here. And what is my weekly base salary? And that is B. So to figure these two things out, we either have to solve this in terms of elimination or substitution. Now, it's really your call. I'm going to use elimination, because the b and b right here is the same. Do you see that? So if I simply just draw a line down here and say, "how about if I just take the first equation and subtract the second equation, the b and b now is gone." Now, I can just focus in on my commission rate, which is the C, right there. So, let's go ahead and figure all the math right here, we got 550 minus 450, which is 100. And 5,000C minus 3,500C is actually 1,500C, right there, okay? And the math I'm gonna solve right here will be just 100 divide by 1,500 and we get ourselves 1 over 15. So the C is just 1/15. So what that's trying to say is that, that's the rate of your commission. I'm getting paid only on 1/15 of the furniture that I've sold. So what is my rate of commission? If you want to change that into decimals, it'll be 0.0666, and if you times it by 100%, that would be 6.66%. So right here, for a, your answer should be 6.67%. Now, for b, what's the weekly salary base? Well, if I know that my C is 1/15, why not take the number and plug it in, let's say the first one or the second one. Let's say I plug it into the first one. So it would be 550 equals to 1/15 of my $5,000 and plus the b. Okay? So if you do that quickly, it will be $5,000 divide by 15, okay? I got $333 here and then take the 550 minus this, you get B. Okay? I got a bunch of fractions, so I'm trying to do all the work with my calculator right away. So my base salary for this one, is actually $216.6 and repeating. But, since this is money, it will be 67, just cross out the repeating sign right here, so it will be just 67. If you want a fraction, it will be just 650 over 3. So that's my base salary right there. I'm going to use the money symbol so $216.67. Okay? So that's how much money the base salary that I get is. Even selling nothing at all, I still get $216.67. Now, for the last part right here: how much does he earn if he sells $7,000 worth of furniture in one week? So we're trying to figure out the final amount that I earned if I can sell this much. Well, I already know the commission, and I know my base salary right here. So what that means is, this is what I'm earning, so I'm gonna put earn right here. And, I'm going to make that equal to the commission rate, which is 1/15 of my $7,000 worth of furniture that I've sold, plus my base salary, which is $216.67. And because of that, I will be taking the 1/15 times $7,000 plus the $216.67, and I got myself $683.34. Pretty good, hey? Hopefully I will survive since he's been given such an expensive place to live in. Okay. There you go. Those are your answers. Thanks for watching.


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