Linear function word problems — Basic example

- [Narrator] A college bookstore charges $60 for a yearly membership, the first book is free with the membership and any book after that costs $7.60 including tax. How much money M does a student spend after buying B books and a yearly membership? So, M, the amount of money that they're going to spend, it's going to be the yearly membership, which is $60, so we're going to do everything in dollars, $60 plus the amount that they spend on books. So, they're going to buy B books, and it's $7.60 per book, so it might be tempting to say, "Alright, you know, I'm gonna have, I'm gonna do $7.60 "per book and then multiply that time B books." So this right over here might be very tempting, but we have to remember something. The first book is free, the first book is free. So, if you buy one book, you're not going to pay $7.60, you're gonna pay nothing. If you buy two books, you're not going to pay $14.20, you're only going to pay $7.60. So, you're only going to pay for one less than the number of books you buy. So, instead of $7.60 being times the number of books, it'd be $7.60 times one less than the number of books you buy. One way to think about it is, this B minus one, you can think of this as books you need to pay for, books that are not free, I guess, books that are not free. The first book is free, and every one after that you would pay for, and this makes sense, if B is two, two minus one, you're gonna pay for one book, if B is 10, that means you're only gonna have to pay for nine books, nine times 7.60, plus the membership. Alright, now let's see which of these choices actually match what we just wrote. So, this one doesn't, it doesn't even include the membership and doesn't take one from the B to account for the free book. This one over here, it does account for the free book but it doesn't account for the membership, so you don't wanna do that. This one accounts for the membership, but it doesn't account for the free book. And then we have this one here, which is exactly what we wrote, except they just swapped, if you just swap these two terms, if you do $7.60 times B minus one, plus 60. So, we're gonna go with that one right there.