Change in euro coins

- [Instructor] We are told that Tim changes a 20 Euro bill for coins. He gets five two Euro coins and the rest in 50 cent coins. How many 50 cent coins does he get? And what's really going on here is he gives someone a 20 Euro bill that would look like this. It wouldn't have specimen written on it. They write that so that I can't print this out and then use it as fake money. And then he wants to convert it into coins. He is able to get five two Euro coins that you see right over here, and then the question is is how many 50 cent coins does he get? So the 20 Euro bill is equal to five two Euro coins plus how many 50 cent coins? Pause this video and see if you can figure that out. All right. So what we really need to do is make the right-hand side here add up to 20 Euros. So the five Euro coins that they talk about right over here, the five Euro coins that he gets in exchange or part of the change, what is that worth? What is this right over here worth? Well, five two Euro coins is going to be worth two, four, six, eight, 10. So this right over here is worth 10 Euro. And so whatever he gets in 50 cent coins has to add up to the remainder. And so what do the 50 cent coin have to add up to? I'm assuming he's going to have a bunch of them, so I'll make a big box right over here. Well, these would have to add up to another 10 Euro, because 10 Euro plus 10 Euro is equal to 20 Euro. So how many 50 cent coins add up to 10 Euro? Well, if I wanna add up to 10 Euro, it's going to have to be 10 Euro times two 50 cent coins, 50 cent coins, coins per Euro, per Euro, and this is 50 cent coins per Euro. And so we're going to need 20 50 cent coins. So the answer here is going to be 20. And you can verify that this all makes sense. You have 10 Euro here, and if we want, we can count this up. This is one Euro. This is two Euros. This is three Euros, four Euros five Euros, six Euros, seven Euros, eight Euros, nine Euros, and 10 Euros. So you can see, and these are 20 coins right over here. So 20 50 cent coins get us 10 Euros. We had another 10 Euros in two Euro coins. 10 plus 10 is, of course, equal to 20 Euros.