SOLUTION: A group of dogs and ducks have a total of 99 heads and legs among them. There are twice as many ducks as there are dogs. How many are there of each animal?

Question 337490: A group of dogs and ducks have a total of 99 heads and legs among them. There are twice as many ducks as there are dogs. How many are there of each animal?
Found 2 solutions by stanbon, benazir.sj@gmail.com:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A group of dogs and ducks have a total of 99 heads and legs among them. There are twice as many ducks as there are dogs. How many are there of each animal?
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Equations:
Since # of ducks = 2(# of dogs)
Head count: 2d + d
Leg count: 2(2d) + 4d
-------
Equation:
2d+d+2(2d)+4d = 99
2d+d+4d+4d = 99
11d = 99
d = 9 (# of dogs)
2d = 18 (# of ducks)
=======================
Cheers,
Stan H.
Answer by benazir.sj@gmail.com(109) (Show Source): You can put this solution on YOUR website!
A group of dogs and ducks have a total of 99 heads and legs among them. There are twice as many ducks as there are dogs. How many are there of each animal
solution:
let Dogs =X
Duck =Y
Dogs having 4 legs and 1 head
=>4X+1X=5x
duck is having 2 legs and 1 head
=>2Y+1Y=3Y
given total legs and heads =99
5X+3Y=99--------------(1)
also given
ducks =2 dogs
Y=2x----------(2)
substitute the value of Y in (1)
5X+3Y=99
5X+3(2X)=99
5x+6x=99
11X=99
X=99/11
x=9
y = 2X
Y=2*9
Y=18
there are 9 dogs and 18 ducks

Proof:
x=9,y=18
5x+3y=99
5*9+3*18=99
45+54=99
99=99
RHS=LHS
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