Uhtred is filling up bags with jelly beans. Each bag requires 22 jelly beans to fill it and Uhtred has 800 jelly beans in total. Part a) Work out the maximum number of bags of jelly beans that Uhtred can fill. Part b) After filling as many bags as possible, how many jelly beans would Uhtred have left over?
For part a, we want to work out what’s the maximum number of bags that can be filled. Well, if Uhtred has 800 jelly beans and there are 22 jelly beans per bag, then the calculation that we need to do is 800 divided by 22 because there’s gonna be 22 jelly beans in each bag. Well, when we’re working that using a calculator, we get 36.36 recurring. And the 36 recurring or 36 with two dots on it means that it continues as 363636 indefinitely. So that’s what recurring means.
Okay, so does that mean that the maximum number of bags that can be filled is 36.36 recurring? Well, no, because we want the complete bags filled. So therefore, we can fill 36.36 recurring which means that we can fill 36 bags. But there isn’t quite enough to fill the 37th bag. So therefore, we round down to 36. And we can say that the maximum number of bags of jelly beans that Uhtred can fill is 36 bags. Okay, so now, we can move on to part b.
Well for part b, we want to see how many jelly beans would be left over. Well, to work this out, the first thing we want to do is work out the total number of jelly beans that will be used in 36 bags. So to do this, we’re gonna do 36 multiplied by 22. And this gives us 792. So therefore, we can say that the beans left over is gonna be equal to 800 minus 792. That’s because 800 is the total number of jelly beans that Uhtred had and 792 is number of jelly beans in 36 bags. And when we subtract 792 from 800, we get eight. So therefore, we can say that Uhtred would have eight beans left over once she’s filled the 36 bags.