Answer:
22 rabbits and 50 hens
Explanation:
Let H and R stand for the numbers of Hens and Rabbits. Each hen has two feet and each rabbit has four feet. Each only has 1 head.
We can set the quantities of feet and heads:
Hens: 2H feet and 1H heads
Rabbits: 4R feet and 1R heads
We are told that:
1.) "The number of feet of the hens exceeds the number of feet of the rabbits by 12" Rewrite this as an expression:
2H - 4R = 12 [feet]
2) "while the number of heads of the hens exceeds the number of the heads of the rabbits by 28" This is written as:
1H = 1R + 28 [heads]
Since each critter only has one head, this last expression will tell us, quickly, how many more Hens there are, which is 28. But by substituting the first expression (the feet) into the second, we can detrermine the exact number of each animal.
Rearrange 2H - 4R = 12 to isolate one of the variables. I'll choose H:
2H - 4R = 12
2H = 12 + 4R
H = (12 + 4R)/2
H = 6+2R
Now use this definition of H in the second equation:
1H = 1R + 28
1(6+2R) = 1R + 28
6 + 2R = 1R + 28
R = 22 There are 22 rabbits
Use this in the second equation to find the number of hens:
1H = 1R + 28
1H = 22 + 28
H = 50 There are 50 hens.
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Check:
1.) "The number of feet of the hens exceeds the number of feet of the rabbits by 12."
Hens have 100 feet total. Rabbits have 88 feet. The hens have 12 more total feet: This checks
2.) "while the number of heads of the hens exceeds the number of the heads of the rabbits by 28"
There are 50 heans and 22 rabbits. The number of hen heads exceed the number of rabbit heads by 28. This also checks.