SOLUTION: how to solve this question using algebraic formula: There are 26 heads and 74 legs, how many chicken and sheep in the farm?

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Question 204160: how to solve this question using algebraic formula: There are 26 heads and 74 legs, how many chicken and sheep in the farm?
Found 3 solutions by Alan3354, ichudov, MathTherapy:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
how to solve this question using algebraic formula: There are 26 heads and 74 legs, how many chicken and sheep in the farm?
------------------------
c = # of chickens
s = # of sheep
-----------------
Chickens have 2 legs, sheep have 4. They all have 1 head each.
Legs = 2c + 4s = 74
c + 2s = 37 (divided by 2)
c + s = 26
-------------- Subtract
0c+ s = 11
There are 11 sheep.
26-11 = 15 chickens.

Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
We'll use substitution. After moving 1*sheep to the right, we get:
1%2Achicken+=+26+-+1%2Asheep, or chicken+=+26%2F1+-+1%2Asheep%2F1. Substitute that
into another equation:
2%2A%2826%2F1+-+1%2Asheep%2F1%29+%2B+4%5Csheep+=+74 and simplify: So, we know that sheep=11. Since chicken+=+26%2F1+-+1%2Asheep%2F1, chicken=15.

Answer: system%28+chicken=15%2C+sheep=11+%29.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

Let the amount of chickens be c, and the amount of sheep be s
Since there are 26 heads, then we’ll have: c + s = 26
Since there are 74 legs and since chickens have 2 legs, while sheep have 4, we’ll then have: 2c + 4s = 74

We now have he following 2 simultaneous equations:

c + s = 26 (multiply by – 2) -----> - 2c - 2s = - 52
2c + 4s = 74 (multiply by 1) -----> 2c + 4s = 74
Add eq (i) & eq (ii) -----------------> 2s = 22
s = 11

Substituting 11 for s in eq (i), we get: c + 11 = 26
c = 15

Therefore, there are highlight_green%2815%29 chickens, and highlight_green%2811%29 sheep on the farm.

Check:
15 chickens + 11 sheep = 26 heads
(15 chickens * 2 legs) + (11 sheep * 4 legs) = 30 + 44 = 74 legs