math
posted by chelsea on .
I have 50.00 to buy 50 animals. Chickens are .50, cows are 2.50,and birds are 5.00. How many of each animal can i purchase?

Divide each of those numbers by 50

Then you must balance it all out
So 50/.5=100
50/2.5=20
50/5=10 
number of chickens  x
number of cows  y
number of birds 50xy
.5x + 2.5y + 5(50xy) = 50
times 10
5x + 25y + 50(50xy) = 500
5x + 25y + 2500  50x  50y = 500
45x 25y = 2000
9x + 5y = 400
we need integer solutions , where both x and y must be between 0 and 50
clearly (0,80) would be a solution to our equation, but not permitted since we only have a total of 50 animals.
BUT, I also know that the slope of the line is 9/5
so if we decrease the y by 9 and increase the x by 5 we get more integer solutions to our equation:
0 80
5 71
10 62
15 53
20 44
25 35
30 26
35 17
40 8
45 1
but remember that 50xx also has to be a positive whole number
the only combination that works is
x =40, y = 8
then 50xy = 2
so we have 40 chickens
8 cows
2 birds
check:
40+8+2 = 50
.5(40) + 2.5(8) +5(2) = 50
Yeahhh!!!