all right hey everyone welcome to unit 5 Notes 3 we are going to be discussing commissions royalties and peacework pay today because you might run into jobs that deal with commissions and commissions are basically just it's an extra little payment or method of payment where an employer um or an employee I'm sorry receives a percentage of the number of sales produced by that employee so for example if you sell um you know a certain amount of items then you might receive like 20% in commission so you'd receive 20 % of that sales um money royalty um is typically used to talk about you know if you are an author or a musician you receive um based on sales so for example if you are I don't know for example Taylor Swift right she probably get some royalty pay for every I don't know CD in theory if we still really use CDs that she would sell right peace workers are um workers who are paid for each item that they produce and there then there's a piecework rate associated with that so it's the amount of money that they get paid for each item that they produce right so if they're producing um shoes or um whatever the case might be Whatever item pencils I don't know what it would be they might receive like I say a couple of cents or a couple dollars extra for that item so let's take a look here at number one who says U Mr girl wrote an updated history textbook for Farmington High School he gets 10% % um royalty based on the total sales of the book so like I say it's a lot of like the authors and the musicians of the world that will get the royalty pay and the book sells for $47.95 and we got 17,000 uh copies that were sold we want to know how much Mr Grove got in royalty payments for the last year so we we need to figure out first of all how much in sales like how much money was made in sales so we're looking for total money which is going to be um I'm going to have to use was this $47.95 cuz that was the cost of each textbook um and then $177,000 were sold so I'm sorry 17,000 copies were sold so that's going to be $47.95 times my 177,000 copies that were sold so that's going to be um a total of 8 15,150 so that's how much money was made off the booker that's how manyy that's how much money was um like brought in from selling the books on in the last year and we know that Mr Grove gets a 10% royalty so now we're going to figure out his commission or his royalty um I'll use the two kind of interchangeably but royalty is specifically for like I say our musicians or like anything like that um so anyway the commission is going to be that 10% of my money brought in so it's going to be 0.1 1 * 8 15,150 so when I multiply those together I end up with 81515 so this is how much money Mr Grove made in the last year based on his royalty pay from the total sales of the book all right number two here says that Ellison sells Cosmetics door to door she has paid a monthly commission uh she receives 11% % of her first $900 in sales and 177% of the balance or the remainder of her sales um so last month she sold $1,250 worth of Cosmetics we want to know how much her commission um or how much she earned in commission last month so the first thing we have to do is figure out um we are told that she gets 11% of the first $900 in sale so let's figure that part out first and to do that we are going to take 11% like I say so 0.11 times the 900 that she sold um originally and I know that she is going to get that 900 because she sold $1,250 worth of Cosmetics which is more than $900 so she is going to get that 900 the 11% of the $900 of course um so then this is going to be $99 so she gets $99 in commission off of just that next we want to find the rest of the commission so let's figure out how much um extra money she sold um or got right so she originally sold 1,250 so 1,250 and then we are going to subtract the 900 that we have already accounted for so that's the 900 and that's going to give me a balance or a remainder of 350 so I am looking for the um the 177% of this amount of money here it's not like I say the total amount of money because we've already accounted for the for the 900 and to do that we are going to go ahead and take take like I say 17% of that so 0.17 * my 350 which is going to give me 59 50 now I want to figure out how much total she earned in commission so I need to take both of these amounts and I'm going to add those together so Al together she ended up making $158 and 50 in Commission in the last month all right so we got Mr Meyer here as a side gig he you know is a local shoe Enthusiast um he um assembles designer sneakers at a factory just as like I say a side gig he has paid a piecework rate of $85 per pair of sneakers produced yesterday he made three pairs of sneakers how much did he earn so like I say this might seem like a very simple problem but again just kind of Common Sense things um so he um made three pairs of sneakers or three pairs of shoes so you have three times um our hourly or our pieace work rate right because like I say it's $85 per pair of shoes so we're going to take that three times the 85 and that ends up being $ 255 so that's how much money he made from working yesterday and making those three pairs of shoes number four here says that Tony picks corn on the Donnelly farm he gets paid 45 cents per container of corn for the first 200 containers filled and then he gets 65 cents for every container over 200 that he fills um last week he filled 270 containers so we want to figure out how much he earned so this is very similar to the one that we did just two problems ago it's just it's instead of percentages it's like an actual amount um so we are told like I say for the first 200 containers and he filled more than 200 containers right so we filled 270 so for the first 200 we're going to use this 45 cents per um container so it's going to be 0.45 again it's 45 cents per container for the first 200 so I'm going to multiply that by 200 and that is going to give me 90 so $90 and then he also um filled an additional 70 so we want to then find the remaining 70 so um if his extra pay is the 65 cents per every container over over 200 again that's going to be 70 so I'm going to do 0.65 or 65 cents times the rest of the containers that we filled which is going to be the 70 that's going to end up giving me 45 so $45.50 and then again we want our total pay for Tony here so I'm going to go ahead and add those together and I end up then with $ 13550 number five here says that Jeff Bowers pays commission to its salespeople um they are paid a percent of the profit the dealership makes on the car um not on the selling price of the car so it's the profit not the actual the the selling price okay the profit is under 750 the commission rate is 20% if the profit is at least 750 and less than or equal to a th000 the commission rate is 22% of the profit and now then if the profit is above $1,000 the rate is 25% of the profit if x represents the profit we want to write a um the commission C of X as a peace wise function okay so all we're doing here is looking for the PE wise function so I'm going to start with C of X and this is going to be equal to like I say PE wise function now we actually have three different things here right because we are we are given um the if it's under 750 right the commission rate is 20% if it's between 750 50 and 1,000 it's 22% and if it's over 1,000 then it's 25% of the profit so we got to like like I say account for three different things so if it's like I say under 750 then it's 20% or02 of the profit which is X so that is when X is less than or equal to 750 okay um next we are going to look at the 22% of the profit so that's going to be 0.2 2 x and that is going to be when again that says when X is or it's at least 750 and less than or equal to 1,000 so we want to say it's between those two numbers so what I like to do is kind of make we can't just write it like 750 to 1,000 right in math land that says 750 minus 1,000 doesn't really work that way so we have to write it like I say algebraically and that's going to be um something that looks like this so it's uh 750 is less than x Which is less than or equal to 1,000 so what this says is that X is greater than 750 right it's bigger than 750 but it's also less than or equal to 1,000 okay um I like to think of it it's kind of written the same way as this it's 750 to a th000 with the X in the middle which just said a little bit more mathematically and then last but not least we have our 25% of the profit so it's going to be 0.25x and that is when X is bigger than 1,000 so it's when the profit is above a th000 so when X is greater than 1,000 so I've now got my peie wise function so we could look at that and see how much money somebody would get for a certain profit so if somebody profited you know $11,000 right that would be that would fall in this category if they profited a th000 that falls in here so we would do 0.2 22 * 1,000 all right one more so we've got um Daniel working at Becker Furniture World he is paid on commission he receives 10% of his first $900 in sales and 15% of the balance of his sales so the remainder right um last week he earned 750 so this is saying that he earned $750 in commission we now want the total value of the furniture that was sold so there are quite a few steps here um let's figure F out what the commission would be of the first $900 that he has sold we are assuming that he sold more than $900 worth of furniture um and he probably did so let's go ahead and uh calculate that part out so again I'm looking for the commission of the first 900 so that's going to be like I say 10% of that first $900 in sale so that's going to be 0.1 * 900 and I'm just going to leave that as it is for right now I can come back and deal with that a little bit later next I'm going to find my balance remaining after the 900 so that would be um if I don't know how much we sold right that's going to be my X cuz I don't know like I say my total value of the furniture sold so that's going to be my x minus the 900 right and again just thinking about this like I say if we sold $900 Worth right let's say we let's say he sold I don't know $2,000 worth of furniture right that $2,000 is kind of what we're looking for that's what we don't know right so to find my remaining balance I would take the 2,000 minus the 900 so I'm just going to replace that with an X so we have something that we can solve for later next we are going to be looking for the commission on the remaining balance so again I know that my remaining balance is this x - 900 and then the commission on that is going to be 15% of that so I'm going to take 0.15 and I want to multiply that by my x - 900 again that's because it's 15% of that and now we can go ahead and find our total commission which is going to be um an equation that we're going to write so basically to find our total commission it's going to be the commission of that first $900 so it's going to be 0.1 * 900 right then we're going to add the commission on the remaining balance so plus my 0.15 * x - 900 and this is going to equal then our total commission but we know our total commission was $750 so this is going to be equal to$ 750 now this is something that we can solve pretty straightforward um right I'm going to go ahead and take my 0.1 * 900 that gives me 90 plus and then I can go ahead and distribute that to get 0.15 xus 135 equaling 750 then I can combine my like terms here so combine my 90 and my - 135 so I end up with 0.15 x - 45 equaling 750 and then from here it's pretty straightforward we're going to add the 45 and divide by 0.15 and then I end up with X equaling 5,300 so I know then that Daniel sold $5,300 worth of furniture in that month if he was able to to make $750 in his commission all right so that was your last example if you have any questions about this at all please let me know otherwise go ahead and work on your homework assignment