Posted by **chelsea** on Monday, May 6, 2013 at 11:04pm.

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?

- math -
**Zaid**, Monday, May 6, 2013 at 11:07pm
Divide each of those numbers by 50

- math -
**Zaid**, Monday, May 6, 2013 at 11:17pm
Then you must balance it all out

So 50/.5=100

50/2.5=20

50/5=10

- math -
**Reiny**, Monday, May 6, 2013 at 11:33pm
number of chickens --- x

number of cows ------- y

number of birds -------50-x-y

.5x + 2.5y + 5(50-x-y) = 50

times 10

5x + 25y + 50(50-x-y) = 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 50-x-x also has to be a positive whole number

the only combination that works is

x =40, y = 8

then 50-x-y = 2

**so we have 40 chickens
**

8 cows

2 birds

check:

40+8+2 = 50

.5(40) + 2.5(8) +5(2) = 50

Yeahhh!!!

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