A riddle about Fanny Farmer's famous Chickens?!
Question: At Famous Fanny Farmer's Market, I can buy chicks for $.50 each, chickens for $1 each, and roosters for $5 each. If I have $100 to spend, how can I buy exactly 100 animals (including at least one animal of each kind) and spend $100?
In how many ways could that be done?
Answers: At Famous Fanny Farmer's Market, I can buy chicks for $.50 each, chickens for $1 each, and roosters for $5 each. If I have $100 to spend, how can I buy exactly 100 animals (including at least one animal of each kind) and spend $100?
In how many ways could that be done?
Let the no. of chicks, chickens and roosters be x, y and z respectively.
0.5x + y + 5z = 100
x + y + z = 100
x + y + z = 0.5x + y + 5z
0.5x = 4z
x = 8z
This means that the no. of chicks is 8 times the no. of roosters.
The cost of 1 rooster and 8 chicks is $9. Treating 1 rooster and 8 chicks as one unit, there cannot be more than 11 units if the total cost of the animals is not to exceed $100.
Therefore there are 11 ways for you to buy the animals.
1 rooster, 8 chicks, 91 chickens
2 roosters, 16 chicks, 82 chickens
3 roosters, 24 chicks, 73 chickens
4 roosters, 32 chicks, 64 chickens
5 roosters, 40 chicks, 55 chickens
6 roosters, 48 chicks, 46 chickens
7 roosters, 56 chicks, 37 chickens
8 roosters, 64 chicks, 28 chickens
9 roosters, 72 chicks, 19 chickens
10 roosters, 80 chicks, 10 chickens
11 roosters, 88 chicks, 1 chicken
Phew! Best answer?
too many ways to count.
uuumm.. i dont know, a lot i guess.