The Turkey Problem:

If a family and a half (1 ½ family) can eat a turkey and a half (1 ½ turkey) in a day and a half (1 ½ day),

how many families can eat six turkeys in six days?

Haha sorry its not corgi related but i am wondering if anyone can figure this one out!

 

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Comment by Emily & Daisy on November 19, 2012 at 7:01pm

Thanks For The Explanation John!

Comment by Julia on November 19, 2012 at 3:43am

Mr. Wolf, this smart-ass was about to type in "6" before seeing your nice long post on the subject. I made a point to just skip to the end to make sure I wouldn't be embarrassing anyone with my simple answer. Seeing that your formula had already made allowances for the smart-ass in the back of the room, I feel comfortable in my initial response. 6.

Comment by John Wolff on November 19, 2012 at 2:31am

The key is to note that this is the same as asking how many families are needed to eat 1 turkey in 1 day (6 turkeys/6 days = 1 t/d). 1.5 turkeys in 1.5 days = 1.5 t / 1.5 d = 1 t/d   i.e., 1 turkey per day.

It takes 1.5 families to do that, so the rate is 1 turkey per day per 1.5 families, or 2/3 = 0.667 turkeys per family-day:

1 t/d divided by 1.5 families = 0.67 t/f-d. 1 family can eat 0.67  (2/3) turkeys in one day.

Let R = consumption rate, 2/3 turkeys per family-day = 0.67 t/f-d

Let F = # of families (we want to solve for this).

Let D = # of days (this factor disappears, since D=1, see above).

Let T = # of turkeys eaten (this factor likewise disappears, since T=1, see above).

T = R x F x D = R x F

1t = 0.67t/f-d x F x 1d   (note that the units "t" for "turkeys" and "d" for "days" both cancel out):

1 = 0.67/f x F

{kids: to solve for F, divide each side of the equation by 0.67t/f-d; you can always multiply or divide both sides of an equation by anything you want without changing it:  Identity Propeyrt of Multiplication: if a=b, ax = bx}

1 / 0.67/f  =  F

1.5f          = F

So it takes 1.5 families minimum to eat 1 turkey in one day.  They do that 6 days in a row.

Note the hidden assumption that the rate remains constant!  Our unexamined assumptions are what get us into trouble.  Even a corgi might be kinda stuffed by, say, Day 4.  R might diminish, increasing D and/or F.  Might need more time and families.

Note the hidden assumption that corgis are absent.  That would change everything.

<smartass kid in back row raises hand>  

"Hey, Mr. Wolff, wouldn't it be a lot easier to simply note that if 1.5 families can eat 1.5 turkeys in 1.5 days, they can eat 1 turkey in 1 day, and thus 6 turkeys in 6 days?"

doh.

Mr. Marko taught me how to do this in 9th grade Algebra I.  He ran off with one of his teenaged students.

Comment by Emily & Daisy on November 18, 2012 at 11:07pm

Haha. I should e-mail my math teacher that! I will be like, wouldnt they be sick of turkey by then? I bet my Daisy wouldnt! No respectable corgi would. lol

Comment by Miranda~ Moses | Maya | Maverick on November 18, 2012 at 6:08pm
Haha I stared at this for a while thinking it was obvious... Then I had like 4 answers... Then I wondered how these turkeys were cooked and if there was pumpkin pie for dessert and if any of these families were venturing out on Black Friday... Then I started thinking about what I want for Christmas. Haha my mind wanders a little too much. Would the answer just be one family? If the ratio is 1:1:1 for the variables, and the days/turkeys are the same, wouldn't one family be able to eat at the rate necessary? I would get sick of turkey by then myself. Is getting sick of turkey a factor? ;-) Good luck!

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