How many 12-ounce bags of nuts can be filled from a three-pound one?
In this problem, we have two measurements of maths. We have a three-pound bag of nuts. Let’s represent this amount by drawing this bar. And then we’ve got some smaller bags that are measured in a different unit of measurements. These are 12-ounce bags. And we need to calculate how many of these 12-ounce bags can we fill from a three-pound bag. In other words, how many lots of 12 ounces are there in three pounds? As we’ve said already, the two units of measurement that we’re dealing with are different. So it would help us to begin with, to think about how many ounces there are in one pound. And perhaps, we could use this to help. One pound is worth 16 ounces.
So let’s alter our bar model slightly. Each of the pounds that make up three pounds is worth 16 ounces. So we can label our three parts as 16 ounces. Now, there’s more than one way we can find the answer to this question. We could calculate the answer. First, we could multiply 16 by three. This would give us the number of ounces that there are in three pounds. And then we could divide this amount, whatever it is, by 12. And this would give us the number of 12-ounce bags we could get from three pounds. Perhaps, this is a method you’d like to try yourself. But there’s actually a quicker method when you use reasoning to help us.
We started of by drawing a bar model. So let’s continue to use this bar model and think about what it means. And this will help us answer the question. Firstly, we can see that each pound, and there are three of them, is worth 16 ounces. Now, the first thing we can say is that 12 ounces is less than 16 ounces. So we can definitely say that we can fill three 12-ounce bags of nuts because 12 fits into 16 with a bit of a remainder. Now, what is each one of these shaded parts worth? 16 take away 12 leaves us with four. So each of the shaded parts of our bar model is worth four ounces, and we have three of them. And what’s three times four worth? It’s worth 12 ounces in total. That’s another bag of nuts.
So we’ve used our bar model to help us solve the problem. One pound is worth 16 ounces. And in three pounds, we have three lots of 16 ounces. In each lot of 16 ounces, we can definitely fill one 12-ounce bag. And we have four ounces spare. And if we add up the three lots of four ounces spare, that makes another lot of 12 ounces, which will fill another 12-ounce bag of nuts. The number of 12-ounce bags of nuts that could be filled from a three-pound one is four. The answer to the problem is four bags.