# Cow word problem

• May 25th 2008, 11:54 AM
annie3993
Cow word problem
A farmer owns several dairy cows, some black, some brown. He finds that 4 black cows and 3 brown cows give the same amount of milk in 5 days as 3 black cows and 5 brown cows give in 4 days. Which gives more milk in a day, a black or brown cow? Show work/explain.

AND

CAn you come up with a rectangle whose sides are whole numbers and whose area is numerically equal to its perimeter? There are 2 solutions.
Area=
Perimeter=

THANKS!!!!
• May 25th 2008, 12:00 PM
sean.1986
Quote:

Originally Posted by annie3993
A farmer owns several dairy cows, some black, some brown. He finds that 4 black cows and 3 brown cows give the same amount of milk in 5 days as 3 black cows and 5 brown cows give in 4 days. Which gives more milk in a day, a black or brown cow? Show work/explain.

AND

CAn you come up with a rectangle whose sides are whole numbers and whose area is numerically equal to its perimeter? There are 2 solutions.
Area=
Perimeter=

THANKS!!!!

Let b = black, r = brown

(4b + 3r)5 = (3b + 5r)4

20b + 15r = 12b + 20r

8b = 5r

Therefore a brown cow gives more milk in a day.
• May 25th 2008, 12:08 PM
Moo
Moo ? :D

Quote:

Originally Posted by annie3993
A farmer owns several dairy cows, some black, some brown. He finds that 4 black cows and 3 brown cows give the same amount of milk in 5 days as 3 black cows and 5 brown cows give in 4 days. Which gives more milk in a day, a black or brown cow? Show work/explain.

Let X be the amount of milk a black cow produces each day.
Let Y be the amount of milk a brown cow produces each day.

Therefore, 1 black cow produces 5X of milk in 5 days. So 4 black cows will produce 4x5X=20X in 5 days.
Similarly, 3 brown cows will produce 3x5Y=15Y of milk in 5 days.

From the second part (in 4 days), 3 black cows will produce 3x4X=12X of milk in 4 days.
5 brown cows will produce 5x4Y=20Y of milk in 4 days.

Therefore, you have the equality : 20X+15Y=12X+20Y

After some calculations, you should get 8X=5Y

--> $X=\frac 58 Y$

I think you can conclude :)

Moo.
• May 25th 2008, 12:29 PM
sean.1986
Quote:

Originally Posted by annie3993
CAn you come up with a rectangle whose sides are whole numbers and whose area is numerically equal to its perimeter? There are 2 solutions.
Area=
Perimeter=

THANKS!!!!

h = height, w = width

hw = 2h + 2w

w(h - 2) = 2h

w = 2h/(h-2)

w is an integer when h-2 is an integer factor of the integer 2h

We know that 1 will be a factor of 2h, so...

let h-2 = 1, h = 3, w = 6

And we know that 2 is a factor of 2h, so...

let h-2 = 2, h = 4, w = 4