## Thursday, October 28, 2010

### Unguarded Halloween Treats

Halloween evenings are exciting and busy. Your kids are dressed up way in advance and couldn't wait to start trick-o-treating. As soon as first darkness descends, you finally figure our your costume, and get to the streets to walk your kids from house to house making sure candy goes to the pumpkin and not straight into their mouth. But who will stay at home to give away your candy? You decide to leave the giant bowl of candy outside of your front steps. While trick-o-treating with your kids you noticed that this year there are twice as many little kids as older kids walking around. When you return in an hour, the bowl is empty. You are wondering how quickly all the 350 Kit-Kats have gone and how many kids may have stopped by. You are pretty sure little kids took one candy each as they were supervised by their parents. As for the older kids, you suspect that half of them may have snatched two candies. Can you estimate how many kids stopped by your house?

Kim said...

There are 2x little kids as big kids, but the big kids are taking 1.5x as much candy (I'd be surprised if there wasnt one greedy kid who just emptied the bowl, but let's go with these assumptions):

Let L=# of Little Kids
Let B=# of Big Kids

L + 2 B = 350
L + 1.5 (.5L) = 350
(because there are 2x as many little kids)

1.75L = 350
L = 200 (who took 200 pieces of candy)
B = 100
(1/2 of whom took 1 piece,
1/2 2 --> 50*1+50*2 = 150 pieces)

Total kids = 300

(Maria, sorry my Friday morning meeting isn't until a little later -- I'm working toward that 50th puzzle!)

Maria said...

Jessica K. just emailed me her puzzle answer:
Neat puzzle!
Notes:
Setting up the puzzle-
2x times 1 and .5 x times one plus .5x times 2 equals 350
2x + 1.5 x equals 350

X equals 100.

Answer: There are 300 kids. 200 little kids took one candy each, 50
big kids took one candy each, and another 50 big kids took 2 candies
each.

GB said...

There are 2 questions:
How quickly all the 350 Kit-Kats have gone?
How many kids may have stopped by?

Kim gave an answer for the second. For the first, I would also estimate how many children I saw on the circuit. Normally, Trick or Treaters go in the same direction as you are going with your children or going in the opposite direction. Assuming that half go faster than you and half go slower, you can possibly get an estimate of the amount of traffic. I would only assume that the candy would not be gone in the first 15 minutes but more towards the end of the hour.

Maria said...

Ok, I think our next puzzle will be guessing when Kim has this meeting of hers. I say 10.30am EST.

She is fast and she is good!
300 kids in an hour. Absolutely right. 45th point for the Usain Bolt of our Family Puzzle Marathon - Kim!

Tom said...

I get here too late, darn it, Pacific Time.
2y plus 1.5o = 350
y is 100. 200 youngsters and 100 oldsters. Yep.

Kim said...

I can move the meeting if I have to... ;-)

Kim said...

In case I created any confusion, I did have a little mistake in the first line of my answer - when I first read it I missed the part about 1/2 the bigs taking two pieces, and thought ALL the big kids two pieces. So the first line where I put L+2B=350 should have read L+1.5B=350. I realized andn corrected the mistake as I started solving it, but never fixed that first line.

Donna said...

OK....I haven't read any other comments, so may be off the mark with this, but I used algebra. If x is the # of older kids, then 2x is the number of younger kids. So 2x would also be the # of pieces of candy taken by the older kids and 2x the # of pieces taken by the younger kids. That yields an equation of 4x=350, which doesn't work out evenly, so about 88 older kids and 174 younger kids.

Donna said...

OK.....I've got some sort of mental block with this and can't figure out why mine doesn't work. What did I do wrong??

Donna said...

I feel like an idiot....read too quickly. Didn't notice half the big kids took two pieces. Sorry to waste so much space. :)

Maria said...

Do not worry, Donna. We are thrilled to have you here freely expressing your thoughts. If you browse through the old puzzles - you will see how each of us made many stupid or serious mistakes. This all is just for fun and if you have any suggestions on how to enhance it, please email me via contact link at the bottom.

Happy and puzzling Halloween to everyone!