 In this video, we provide the solution to question number three for practice exam number four for math 1030 And we have the following situation a coin jar containing 200 coins Consisting of pennies and nickels, which is one point one cent and five cents respectively So then we have Takashi here draws out 30 coins from the jar and it consists of 12 pennies and 18 nickels So we want to estimate how much currency is inside the jar So we want to estimate how many pennies how many nickels do we have here? So we should look at those percentages. So you got 12 over 30 is our percentage of pennies Okay, for which we can simplify that fraction 12 and 30 are both divisible by six So you could simplify that to be two-fifths right there nickels on the other hand By this estimate we have 18 over 30 again These numbers here are both divisible by six. You get three-fifths. And so you see that about 40 percent of the sample was pennies and the 60 percent of the sample was nickels So if that is a representative proportion, then we can extrapolate that proportion onto the whole population And then go from there to assume. Uh, that's how much money is in the jar there. So 40 percent of 200 there That's giving me how many pennies we get But we also are going to take 60 percent of 200 to get how many nickels I'm going to times that by five because nickels are worth five cents and pennies are worth one cent there so Notice here five goes into two hundred forty times times that by two you're going to end up with eight 80, uh, excuse me 80 pennies. So 40 percent of 200 is 80 similarly I'm going to times it by one because it's worth one penny there Um, so now we need to take 60 percent of 200 for which we can do the same type of thing Five goes into 240 times times that by three you get 120 But I can also make the observation that a 40 percent of 200 is 80 Then subtract that from 200 that leaves you with 60 percent, which is 120. We have to times that by five, of course Because nickels are worth five cents each. Well, 80 times one is pretty easy. That's just 80 here times the other one By five there, uh, you know, you can feel free to use a calculator if you're struggling with the arithmetic here whatsoever But a nice little trick that you could do here is if you borrow a two because 120 is just 60 times two Notice that two times five is 10. That's a whole lot easier. You're going to get a 600 You know, however you want to get through the arithmetic, you're going to get 600 there And so 80 plus 60 600 would be 680. This is going to be cents, of course And therefore we search amongst the answers and we see that the correct answer would then be b There's 680 cents or that is six dollars and 80 cents inside that jar approximately