SOLUTION: Can't figure how to set this up!!?? Practically blind without my glasses, I can only see shapes in the barnyard. Despite that, I count 46 legs, but only 14 heads in a farm yard o

Algebra ->  Expressions-with-variables -> SOLUTION: Can't figure how to set this up!!?? Practically blind without my glasses, I can only see shapes in the barnyard. Despite that, I count 46 legs, but only 14 heads in a farm yard o      Log On


   



Question 466372: Can't figure how to set this up!!??
Practically blind without my glasses, I can only see shapes in the barnyard. Despite that, I count 46 legs, but only 14 heads in a farm yard of sheep and geese. How many of each are there?

Found 2 solutions by stanbon, MathLover1:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
I count 46 legs, but only 14 heads in a farm yard of sheep and geese.
How many of each are there?
---
Animal equation: s + g = 14
Leg equation::: 4s + 2g = 46
-------------------------------
Divide thru the leg equation by 2:
s + g = 14
2s + g = 23
---------------
Subtract and solve for "s":
sheep = 9 (# of sheep)
----
Solve for "g":
s + g = 14
9 + g = 14
g = 5 (# of sheep)
=========================
Cheers,
Stan H.
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Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
let sheep be x and gees y
sheep has 4 legs: 4x
gees have 2 legs: 2y
there are 46 legs: 4x%2B2y=46

but only 14 heads: x%2By=14
4x%2B2y=46
x%2By=14
--------------------solve this system
x%2By=14....solve for x
x=14-y......substitute in 4x%2B2y=46

4%2814-y%29%2B2y=46

56-4y%2B2y=46

56-2y=46

56-46=2y
10=2y
5=y
sheep and 5 gees