SOLUTION: Cows cost $10, pigs cost $3 and chickens cost $0.50. A man buys 100 animals for $100. How many of each animal does he have? he must have at least one of each animal.

Question 108883: Cows cost $10, pigs cost $3 and chickens cost $0.50. A man buys 100 animals for $100. How many of each animal does he have? he must have at least one of each animal.
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
C = number of cows
P = number of pigs
Ch = number of chickens
C + P + Ch = 100
10C + 3P + .5Ch = 100
Ther are 3 unknowns and only 2 equations, so there is no direct solution
multiply both sides by 2
20C + 6P + Ch = 200
subtract the 1st equation from this one
20C + 6P + Ch = 200
C + P + Ch = 100
19C + 5P = 100
All you need to apply is some number sense. The 2nd term, 5P
will either end in 5 if P is odd, or 0 if P is even.
So if P is odd, 19C has to end in 5 for the sum to end in 0.
If P is even, 19C has to end in 0.
Here's some combinations:
------------------------
P = 5
5P = 25
C = 5
19C =95
19C + 5P = 100
95 + 25 = 120 -too much
----------------------------
P = 3
5P = 15
C = 5
19C = 95
19C + 5P = 100
95 + 15 = 110 -still too much
----------------------------
P = 2
5P = 10
C = 10 (note that 10 is the smallest # of cows that makes 19C end in 0)
19C = 190
19C + 5P = 100
190 + 10 = 200 -way too much
----------------------------
P = 1
5P = 5
C = 5
19C = 95
19C + 5P = 100
95 + 5 = 100 this is the answer
-----------------------------
Now find Ch and check both equations
C + P + Ch = 100
5 + 1 + Ch = 100
Ch = 94
-------
10C + 3P + .5Ch = 100
50 + 3 + 47 = 100
100 = 100
So, there are 1 Pig, 5 Cows, and 94 Chickens
RELATED QUESTIONS
Cows cost $10, pigs cost $3 and chickens cost $0.50. A man buys 100 animals for $100. How (answered by ankor@dixie-net.com)

Old Mcdonald was buying animals for his farm. Cows cost $10, Pigs cost $3, and chickens... (answered by ankor@dixie-net.com)

When young MacDonald was starting his farm a long time ago, cows cost $10 each, pigs cost (answered by ptaylor)

when young MacDonal was starting his farm a long time ago,cows cost $10 each,pigs cost $3 (answered by ankor@dixie-net.com)

a famer has $100 doallrs to spend on 100 animals. he has to end up with 100 animals.... (answered by KMST)

u buy 100 animals for $100, cows cost $10,pigs cost $1.75 and chickens cost $.50 how many (answered by ikleyn)

Farmer wants to buy cows, pigs and chickens. He has $100 and wants to buy total of 100... (answered by josmiceli,richwmiller)

A farmer has bought 100 animals for $100. He has bought cows, pigs and chickens. If the (answered by Paul)

A farmer has 100 animals consisting of cows, pigs and chickens. He takes the animals to... (answered by ankor@dixie-net.com)