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Thursday, December 19, 2013

Puppy Chow Math Test

Just a little project this morning to make some fun packages to take to people at work. At some point I realized I was doing several elementary school math story problems to complete the project. (and one a little more complex) I don't understand people who say they never use math. So here's a quiz for you. Answers at end.

I decided to make "puppy chow" snack mix for everyone.

Q1. How many people actually work in the mail room and on the presses?

Q2. Which is the better value? A 3-pack of red curly ribbon for 79¢ or a 6 pack of assorted colors for $1.35? The spools of ribbon are all the same size.

Q3. If the recipe calls for 8 oz each of rice and corn chex, but you want to add Cheerios too, and you are going to double it, and the rice chex is an 18 oz box, and the corn chex is a 14 oz box, and the Cheerios is a 16 oz box, how many boxes should you buy?

mixed cereal

Q4. If the recipe calls for ½ c. peanut butter, but you are going to double it, and you have an 18 oz jar, how much should you use? (You melt the p.b. with oleo and chocolate chips.)

chocolate in pan

Q5. How big a pan or bowl will you need to mix it all?

puppy chow

Q6. The recipe calls for ½ c. powdered sugar, but you are doubling the recipe. How much powdered sugar will you need?

Sorry, no picture of the finished product, but here's the bag with sugar in it. You add the chocolate coated cereal and shake it up to give it a sugar coating too.

bag of sugar

Q7. How many gift bags can you fill with what you just made?

gift bags of puppy chow

Q8. With 6 spools of ribbon, each labeled as 10m long, if you use 2 arm lengths for each bow, will you have enough ribbon?

Q9. How many combinations of two colors can you make without repeating any of the combinations?

Q10. How much did this gift cost per person? The 3 boxes of cereal cost $2.99 each, and I had a $1.00 off coupon (not per box). The 2 bags of chocolate chips were $1.99 each. The peanut butter was $1.88 for the 18 oz jar and I had a 75¢ off coupon. The oleo was 88¢ a pound and I used 2 sticks. The sugar was $1.89 for 2 pounds, and I used about ¼ pound. The plastic bags cost $2.00 for 50 bags. The paper bags cost about a penny each (had on hand), and the ribbon was $1.35 for the six spools.

A1. It would have been intelligent to ask someone, eh? O well, I decided to make a double batch and hope it would be enough. This is called estimating. I think this was an 8th grade lesson.

A2. 79/3= 26.3¢ each. 1.35/6= 22.5¢ so the 6 pack is the better value. Quick and dirty method: 79*2= $1.58 which is more than $1.35, so the 6 pack is cheaper. And more colors is nice anyway.

A3. One of each, because you are going to just dump it all in and not worry about measuring this stuff. This is not a fussy recipe, and you have a coupon for $1.00 off if you buy 2 boxes of cereal.

A4. You need ½*2 = 1 cup peanut butter. There are 8 oz in a cup, and half the jar of p.b. is 9 oz, so just use about half the jar. Please don't mess up a measuring cup to do this. This is not a fussy recipe.

A5. This answer requires you to know more about the density and bulk of the product, not the weight. Trial and error works as well as anything. The answer is- the two biggest pans you own, so there's room to mix the chocolate and coat the cereal.

A6. You thought this was going to be an easy one, right, as in ½*2= 1? Haha. The answer is, at least twice that much to properly coat the cereal. Don't believe everything you read in recipes.

A7. Just do it and see. Then please write the answer on the recipe card so you'll know next time you make this. You can make 18 bags with 5 oz of puppy chow in each one (yes I weighed them). That leaves about 3 oz that fell on the floor for the cook to eat (5 second rule). Just in case you are feeling OCD, it's interesting to note that 50 oz cereal + 9 oz peanut butter + 8 oz oleo + 24 oz chocolate chips + 4 oz powdered sugar = 95 oz of ingredients. 95/5= 19, which is almost exactly what I ended up with, allowing for some product loss that stuck to the pan, etc.

A8. A meter is about a yard. An arm length is about a yard. You have 6 spools * 10 m = 60 meters which equals about 60 yards. You have 18 bags to decorate. 18*2= 36 yards needed. You have plenty of ribbon.

A9. OK, this one isn't a grade school question, it's basic statistics. But the visual answer is in the picture of the bags. The formula is n!/(n-r)!(r)! where n is the number of objects to choose from (6 colors), and r is the number you want to use in each set, which is 2. The ! means multiply the number by every smaller number so n!= 6*5*4*3*2*1. (n-r)! = (6-2)!= 4*3*2*1, and r!= 2*1, so you end up with (6*5*4*3*2*1)/(4*3*2*1*2*1). You can cancel everything out except the 6*5 on top and a 2 on the bottom, so 30/2= 15 different combinations. But the visual answer is seen in the rows. The back row has red combined with every other possible color, so R-L we have red/silver, red/green, red/magenta, red/gold, red/blue. Then the next row forward is blue with every other possible color, so using the same order R-L we have blue/silver, blue/green, blue/magenta, blue/gold. This leaves blue/red, but we've already got that in the back row, so we only have 4 possibilities in this group (It's a whole different math problem if the order matters- in other words, if red/blue is not the same thing as blue/red). The next row forward is gold with every other possible color, so now we have gold/silver, gold/green, and gold/magenta, but that's all we can do that aren't duplicates. Next we do magenta/silver, and magenta/green. Only two new possibilities. Then in the front row is green/silver, and that's all we can do.

A10. Are you still here? Who cares? But quizzes have to have 10 questions, right? And I am curious. I snuck one little assumption in the question, and that is that you know there are 4 sticks of oleo in a pound. OK. {[($2.99*3)-1.00] + (2*1.99) + (1.88-.75)/2 + (.88/2) + [1.89/(2/¼)] + [(2.00/50)*18] + (18*.01) + [1.35*(36/60]}/18 Do each part of the formula {7.97 + 3.98 + .67 + .44 + .24 + .72 + .18 + .81}/18 Continuing 15.01/18 = $0.83 each. Not bad, not bad... everyone loved it. I got mega brownie points, and there was enough to go around, including for the guys running the presses, who often get overlooked when it comes to treats.

I suspect only two of my regular readers actually made it this far. You know who you are!

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Loritenor said...

Math teachers would have loved given this to their students...oh and "estimating" in math is the big thing now along with compatible numbers...or something like that. There are a zillion new terms for everything. I think I had #3 correct...just dump in the three boxes....

Ann said...

My head may be spinning right now but I did make it through the whole post. Now in keeping with the math subject you may need to add 1 to your suspicion if I was not among the two who you thought would make it all the way through....lol

Ann said...

oh and I forgot to say I like the way you make this, that's the way I do it too

The Furry Gnome said...

Well I made it to the end too, though I admit to skipping a word or two. I love your answers, but you lost me with Q.9. Meantime, you left out the most important question - how did it taste? Maybe everything can't be reduced to math?

vanilla said...

My wife always says, "If you can read, you can cook." Apparently math is also required. Oh, well.
(I made it to the end. I do like a good math quiz.) Fun.

Unknown said...

I understand math a lot better now that I have had 52 years of practical experience.

Secondary Roads said...

I read through answer 8. Then the ADD kicked in and I jumped to the final paragraph--and found I'd been busted. Oh well . . .