Creating expressions and equations | Worked example

- [Instructor] We are told that at the start of a convention Melinda had 100 T-shirts, I'll underline the important numbers here, 250 pens, and 500 buttons to give away to convention attendees. By the end of the convention, she had 1/5 the number of T-shirts, 1/5 the number of pens, and none of the buttons remaining. Or another way to think about it, zero buttons remaining. Which of the following computes the number of T-shirts, pens, and buttons Melinda had remaining by the end of the convention? So pause this video and see if you can work through this. All right, now let's do it together. And there's a couple of ways that you could approach it. One way is to just try to come up with an expression that would describe the number of T-shirts, pens, and buttons Melinda has by the end of the convention, and see if that is equivalent to any of these expressions. Another way is you could look at the expressions and see which of these makes sense. So actually let's just do it both ways. So if we just try to generate our own expression, even before looking at these choices, we know that she is left with 1/5 of the original number of T-shirts, and she originally had 100 in T-shirts. So how many T-shirts is she left with now? So she's left with 1/5 times 100. And then how many pens is she left with now? Well she know, or they tell us, that we are left with 1/5 the number, the original number of pens. So that's going to be plus 1/5 times the original number of pens, times 250. And then how many buttons? Well they tell us that she is left with none of the buttons are remaining, so zero buttons. Or we don't even have to write that. We could just write it like this, 'cause if you add zero it obviously doesn't change the quantity. So let's see, do we see 1/5 times 100, plus 1/5 times 250 over here? Well no, we don't see that exactly, but we can see that all of the choices here, it looks like they have some fraction times the sum of some things, and then in some cases they might add something else. So one way to think about it is we could either take these expressions and distribute the, try to distribute the 1/5. Or we could try to factor out the 1/5 here to make this look more like one of these choices. So let's do that. So if we factor out 1/5, this is going to be the same thing as 1/5 times 100, plus 250. Plus 250, which we can immediately see is choice B. Now we could have gone the other way around. We could have started with the choices. We could have said look, choice A has 1/5 times the sum of our original number of T-shirts, pens, and buttons. And that would have been accurate if we were left with 1/5 the number of T-shirts, 1/5 the number of pens, and 1/5 the number of buttons. But they say that none of the buttons are remaining. So we know that this is going to be wrong, because we have the, we're essentially saying that 1/5 of the buttons are remaining. 1/5 times 500, that'd be 100 buttons remaining, and they say none of the buttons are remaining. Here we have 1/5 times the number of T-shirts and pens, but then we just have the original buttons, and that is almost the opposite of what they're saying. They're saying we have no buttons remaining versus 500, so we could rule that out. This one is saying 4/5 of the number of T-shirts and the number of pens. Well once again, that's not what they told us. They told us 1/5 of the number of T-shirts and the number of pens. You could rule that out. Now this is doing 1/5 of times the number, the original number of T-shirts, but then for some reason they're multiplying that times the number of pens. And so that one just mathematically is not what they're describing there. So we could rule that one out as well.