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Math Fun #1137453
01/04/18 06:22 PM
01/04/18 06:22 PM
Joined: Aug 2000
Posts: 52,940
Upstate NY
Pandora Offline OP
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Pandora  Offline OP
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Please show your work! smile

-1. There are several chickens and rabbits in a cage (with no other types of animals). There are 72 heads and 200 feet inside the cage. How many chickens are there, and how many rabbits?

-2. You've been asked to buy 100 squeegies, using 100 dollars to do so. You may buy no more or less than 100 squeegies, and the total price must be exactly 100 dollars. There is no sales tax. Red squeegies cost $6.00. Yellow squeegies cost $3.00. Blue squeegies cost $0.10. How many of each must you buy?

-3. On a man's tombstone, it is said that one sixth of his life was spent in childhood and one twelfth as a teenager. One seventh of his life passed between the time he became an adult and the time he married; five years later, his son was born. Alas, the son died four years before he did. He lived to be twice as old as his son did. How old did the man live to be?


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Re: Math Fun [Re: Pandora] #1137472
01/04/18 09:01 PM
01/04/18 09:01 PM
Joined: Jul 2002
Posts: 29,024
Unionville
manxman Offline
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1. c=chickens r=rabbits
c+r=72 (1)
2c+4r=200 (2)
2c+2r=144 (3)from(1)x2
2r=56 (2)-(3)
r=28
c=44
44 chickens 28 rabbits wave


Sometimes lost is where you need to be. Just because you don't know your direction doesn't mean you don't have one.
Re: Math Fun [Re: Pandora] #1137476
01/04/18 09:31 PM
01/04/18 09:31 PM
Joined: Aug 2000
Posts: 52,940
Upstate NY
Pandora Offline OP
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Pandora  Offline OP
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I'm hoppy you got that one right, manxman! wave


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Re: Math Fun [Re: Pandora] #1137497
01/05/18 09:27 AM
01/05/18 09:27 AM
Joined: Jul 2002
Posts: 29,024
Unionville
manxman Offline
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2. r+y+b=100 (1)
6r+3y+0.1b=100 (2)
60r+30y+b=1000 (3) 10x(2)
subtracting (1) from (3) gives
59r+29y=900 (r and y must be whole numbers)
solving this gives r=1 and y=29 which means b=70 smile


Sometimes lost is where you need to be. Just because you don't know your direction doesn't mean you don't have one.
Re: Math Fun [Re: Pandora] #1137508
01/05/18 10:39 AM
01/05/18 10:39 AM
Joined: Aug 2000
Posts: 52,940
Upstate NY
Pandora Offline OP
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I'd like a yellow one, please. smile


Netflix needs to stop asking if I'm still watching and start asking if I've switched the laundry over yet
Re: Math Fun [Re: Pandora] #1137530
01/05/18 01:30 PM
01/05/18 01:30 PM
Joined: Nov 2000
Posts: 18,719
Ottawa Ontario Canada
CanukDenis Offline
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CanukDenis  Offline
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Ottawa Ontario Canada
3: Seems to be a "trick" question (make it appear difficult).

x = age at death:
since 1/12 of age was spent as teenager (13 to 19 : 7 year span),
then (1/12)*x = 7 : x = 12*7 = 84



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Re: Math Fun [Re: Pandora] #1137544
01/05/18 06:14 PM
01/05/18 06:14 PM
Joined: Aug 2000
Posts: 52,940
Upstate NY
Pandora Offline OP
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Pandora  Offline OP
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Upstate NY
You spotted the trick, Denis! smile

Of course, it could also have been solved the regular way:

Let x be the age of the man at the time of his death. His age consists of the number of years he spent as a child plus the number of years he spent as a teenager plus the number of years between his coming of age and his marriage plus five plus his son's age (half his own) plus four. In mathematical terms, this is:
x = x/6 + x/12 + x/7 + 5 + x/2 + 4
x = 14x/84 + 7x/84 + 12x/84 + 42x/84 + 9
x = 75x/84 + 9
84x/84 - 75x/84 = 9
9x/84 = 9
x/84 = 1
x = 84


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