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Post by ~Dernhelm~ on Jan 9, 2003 8:14:34 GMT
This one is hard... Yet giving it a try could be worthwhile. I've just found a site with tons of these problems!
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My Three Dogs
My neighbor has three pets in his home, all dogs. Fifi is the little French poodle. The name of my neighbor's big St. Bernard is Maxx. And Sparky, the medium-sized dog, is, well, let's just say he is of no particular breed.
Last week my neighbor took his beloved pets to the vet for their annual health check-ups and shots. The doctor weighed them as part of the examination. Upon returning home, my friend told me the animals' weights in an unusual way. He said:
* "Together Fifi and Maxx weigh 72 pounds."
* "Maxx and Sparky have a combined weight of 86 pounds."
* "Lastly, the sum of Sparky's and Fifi's weights is 35 pounds."
Tell me now how much each dog weighs, individually. Your explanation should use variables and equations to communicate the method you've used to solve the problem.
***
Good luck!
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Post by Balin on Jan 10, 2003 18:36:30 GMT
Not a problem.
Fifi = 10.5
Maxx = 61.5
sparky = 24.5
I will take Fifi first
Fifi = 72 - maxx = 35 - sparky
(72 - Fifi) + (35 - Fifi) = 86
107 - 2 Fifi = 86
2 Fifi = 21
Fifi = 10.5
72 - Fifi = maxx
72 - 10.5 = Maxx
maxx = 61.5
35 - Fifi = sparky
35 - 10.5 =sparky
sparky = 24.5
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Post by ~Dernhelm~ on Jan 11, 2003 12:33:19 GMT
You did it, Balin! Another one?
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Driving to Work
Tracey drives to work at 40 mph and is 1 minute late. If she leaves at the same time and drives 45 mph, she'll be 1 minute early. How far does Tracey live from work?
Your explanation must use algebra (variables and equations) to communicate the method you've used to solve the problem.
Extra: Tracey gets stuck in traffic one morning and only averages 20 miles per hour on the way to work. What speed will she have to average on the trip home so that her average speed for the entire round trip is 40 miles per hour?
***
Good luck once more!
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Post by Balin on Jan 13, 2003 16:48:40 GMT
I think I know where you find your problems
mathforum.org right? I sent in an anser to that problem and I will get it corrected soon do you want that anser posted here to?
btw post 600
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Post by Balin on Jan 13, 2003 16:50:48 GMT
Why not?
I will make some calculations first.
distance
--------- = 40/60
time+1
distance
--------- = 45/60
time-1
(t+1)* 40/60 = (t-1)* 45/60
(t+1)* 40 = (t-1)* 45
40t + 40 = 45t - 45
5t = 85
t = 17
Now I know that it takes 17 min to get to work then I just add one fore the 1 min late
(17+1)*40/60 = 12 miles
Or take away one fore the one min early
(17-1)*45/60 = 12miles
It's hard to see the equation cos' the = is not in line but you get the idea.
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Post by Imrel on Jan 14, 2003 3:16:29 GMT
How did you know to divide by 60?
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Post by Balin on Jan 14, 2003 15:36:33 GMT
60 min in an hour 
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Post by Balin on Jan 14, 2003 15:39:55 GMT
I saw that I missed the extra but thats impossible anyway so why even bother.
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Post by ~Dernhelm~ on Jan 15, 2003 11:59:03 GMT
Aye, I do get them from there. I'm not evil enough to make them up by myself.
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Post by Balin on Jan 19, 2003 16:21:50 GMT
But this one was no anser to there.
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Post by ~Dernhelm~ on Jan 20, 2003 13:58:55 GMT
I don't look at the answer until the problem has a solution... Another one? 
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Post by Balin on Jan 21, 2003 16:35:32 GMT
Sure...
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Post by ~Dernhelm~ on Jan 22, 2003 18:02:18 GMT
Alright. I think the subject of this one is quite funny...
***
Porky Pig's Popcorn Diet - posted August 30, 1999
Porky Pig really loves eating popcorn, but lately he's been getting a bit "pudgy" (fat), so his doctor has put him on a peculiar diet.
Porky can eat one piece of popcorn on the 1st day of any given month, two pieces on the 2nd day, three on the 3rd day, and so on during the month. The next month the whole process will begin anew.
How many pieces of popcorn does Porky pop into his "pucker" (mouth) during the first six months of this year, 1999?
Bonus: What is the name of the famous algebraic formula that should be used to solve this puzzle?
Note: Since this is the Algebra Problem of the Week, it is expected that you will use normal algebra to solve this puzzle. This means that no brute force methods, such as spreadsheets or using a calculator to merely add up the numbers 1, 2, 3, 4, and so on, will be accepted. There is a famous formula that you should know about that 'automatically' finds the sum of an expression like:
1 + 2 + 3 + ... + n = ?
We hope you can find and use it.
***
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