SOLUTION: I need to know how many cats and witches are out in this problem. I know that the number of legs was 3.5 times the number of heads and the total number of heads and legs are 72.

Question 54702: I need to know how many cats and witches are out in this problem. I know that the number of legs was 3.5 times the number of heads and the total number of heads and legs are 72.
Found 2 solutions by checkley71, stanbon:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
WHERE DO YOU GET THAT LEGS IS 3.5 TIMES THE NUMBER OF HEADS.
I GET 2 HEADS WITH A TOTAL OF 6 LEGS WHICH IS 3 TO 1 NOT 3.5 TO 1.
72=X(3)+Y(5)
72=3X+5Y
THIS HAS A FEW SOLUTIONS
6 CATS 14 WITCHES 0R 6*5+14*3=72 OR 30+42=72 OR 72=72
9 CATS 9 WITCHES OR 9*5+9*3=72 OR 45=27=72 OR 72=72
12 CATS 4 WITCHERS OR 12*5+4*3=72 OR 60+12=72 OR 72=72

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
I need to know how many cats and witches are out in this problem. I know that the number of legs was 3.5 times the number of heads and the total number of heads and legs are 72.
----------------
Let "c" be the number of cats.
#of heads on these cats is "c heads"
# of legs on these cats is "4c legs"
----------
Let "w" be the number of witches.
# of heads on these witches is "w heads"
# of legs on these witches is "2w legs"
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Total # of heads is c+w
Total # of legs is 4c+2w
EQUATIONS:
1st: 4c+2w = 3.5(c+w)
2nd: 4c+2w+c+w=72
Simplify 1st and 2nd as follows:
3rd: 0.5c-1.5w=0
4th: 5c+3w=72
---------------
Multiply 3rd by 10 to get:
5th: 5c-15w=0
Subtract 5th from 4th to get:
18w=72
w=4 (this is the number of witches)
Substitute in 5th solve for # of cats, as follows:
5c-15(4)=0
5c=60
c=12 (this is the number of cats)
Cheers,
Stan H.
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