Problem Two - P and J (yummmmmm)

Peanut Butter and Jelly 

As I was making peanut butter and jelly sandwiches the other day, I ran out of bread. I still had half a jar of peanut butter and close to three-quarters of a jar of jelly left. 

As I ran down to the freezer to get another loaf of bread, I started thinking about the number of sandwiches I could make with the individual ingredients. A loaf of bread contains eighteen slices, though we do not like to have the heels (the ends) for our sandwiches so we always feed those slices to the birds. The 16-ounce jars of peanut butter will make 12 sandwiches, and the 48-ounce jars of jelly will make 60 sandwiches. 

(We like a little less jelly than peanut butter so the sandwiches aren't too "oozie"... but we always manage to end up with jelly on their clothes anyway!) 

If we were to start with a full loaf of bread and new jars of peanut butter and jelly, how many sandwiches could we make before emptying a bread bag and jars of jelly and peanut butter at the same time? 

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Puppy Party

Dogs are all related to each other, but they come in 

all different shapes, sizes...and colors.  Dogs can be white, brown, black, grey, spotted, or mixtures of these. But one favorite dog breed is golden: the Golden Retriever. These super-fluffy, super-friendly dogs are so named because they like to fetch animals while out hunting with their owners. In fact, they'll fetch anything you throw, from a ball to a stick to a newspaper. Given their popularity, it's no surprise that goldens get their own party to celebrate their existence. Once a year the Golden Retriever Club of Scotland holds a giant "Golden Gathering" at Guisachan, which is where the breed was officially born. This year, 222 dogs showed up and romped around chasing flying objects and each other. We just hope someone had a lot of treats handy, and a good pooper-scooper.

   

Here’s the problem:

If the dogs are divided into groups of either 3 or 5 to play Frisbee, and you need one Frisbee per group, what's the smallest number of Frisbees you'll need to have on hand?

Solution:
Here is your solution. Check it against your answer, how did you do?
Ms. L.

The smallest number of Frisbees needed are 46. The bigger the groups, the fewer Frisbees you'll have, but 222 isn't evenly divisible by 5. The closest multiple of 5 that leaves a multiple of 3 left over is 210, which gives you 42 groups. That leaves 12 more dogs, who can be divided into 4 groups of 3.

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Ms. Leckman