Answer:
135 boxes
Step-by-step explanation:
First, let's express the information as conversion factors:
There are: (6 bags/1 multipack)
We also know: (8 multipacks/box)
We start with 6500 bags and we want to convert this into boxes. Find a way to use the conversion factors to convert bags into boxes. One of the wonderful things about conversion factors is that you can invert them!
The numerator is equal to the denominator in a conversion factor. So we can write not only (8 multipacks/box), but also (1 box/8 multipacks).
I bring that up here, because we want a conversion factor that will have boxes in the numerator, because we need boxes in the final answer.
Neither of the conversion factors we have so far will convert directly from bags into boxes. But a combination of the two would:
1. Convert bags to multipacks:
Invert the first conversion factor to (1 multipack/6 bags) and multiply it by the 6500 bags:
(6500 bags)(1 multipack/6 bags) = 1083 1/3 multipacks [Note how bags cancel, leaving only multipacks]
We can only use whole numbers of bags in multipacks, so round this to 1083 multipacks.
2. Convert multipacks into boxes:
We have a conversion factor that relates multipacks to boxes: (8 multipacks/box)
We can either divide 1083 multipacks by (8 multipacks/box), or we can invert the conversion factor and then multiply. I'll invert the factor and multiply. It just makes it easier for me to see that multipacks cancel, but you can do either.
I'll use (1 box/8 multipacks)
(1083 multipacks)((1 box/8 multipacks) = 135.375
Again, we will round down to a whole number: 135 boxes.
There are a few bags left over.
Total number of bags used is:
(135 boxes)((8 multipacks/box)(6 bags/1 multipack) = 6480 bags
We have 20 bags left over.
Give them to the work crew (or save them for the next day).
