   SEARCH HOME Math Central Quandaries & Queries  Question from Rogerson, a student: In a certain poultry farm, the ratio of the number of hens to roosters is 3:5. If 15 new roosters are added, a third of the farm will be compose of hens. Find the original number of chickens. Hi Rogerson. Let's translate this into equations and algebraic expressions:

In a certain poultry farm, the ratio of the number of hens to roosters is 3:5.

h/r = 3/5

If 15 new roosters are added,

r + 15

a third of the farm

(1/3)[h + (r + 15)]

will be compose of hens.

= h

Find the original number of chickens.

Find h+r.

Solution:
We have two equations:

(1) h/r = 3/5
(2) (1/3)[h + (r + 15)] = h

We want to know h + r.

The easiest way is to use either substitution or elimination method to find the value of h or r and then find the other value by just plugging that into equation (1). Then add them together to get the answer h + r.

If you want examples of using the "Substitution method" (that's the one I'd choose in this case) or the "Elimination method" of solving simultaneous equations, then type those into our Quick Search.

Hope this helps,
Stephen La Rocque     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.