A farmer has 4 times the number of ducks as dogs with a total of 36 legs. How do you set up equations?
2007-12-04 12:49:12 · 8 answers · asked by rrogers_1 1 in Science & Mathematics ➔ Mathematics
[13]
Let the number of dogs be x
Then the number of ducks is 4x
no of legs are 4x+8x=12x
12x=36
x=36/12=3
Therefore no of dogs=3
No of ducks=3*4=12
2007-12-04 12:56:26 · answer #1 · answered by alpha 7 · 0⤊ 0⤋
ok. so there are 36 total legs.
a dog had 4 legs and we don't know how many dogs there are, so we'll call the dogs X.
so the numbers of legs of dogs is 4X.
There are 4 times the number of ducks as dogs. Ducks have two legs. so there are 4X number of ducks because there are 4 times the number of ducks as dogs (and X represents dogs). Then we have to remember that ducks have to legs. so 2*4*X, which is 8X. so then...
36 = 4X + 8X
4X is the number of dog legs
8X is the number of duck legs.
so 36 = 12X
36/12 = X
so X = 3. There are three dogs.
then there are 4 times as many ducks as dogs, so 4*3 = 12.
There are 12 ducks.
Then check by multplying these answer by the number of legs each species has and adding to see if there are 36 legs.
2007-12-04 12:55:09 · answer #2 · answered by Gabby ^ 2 · 1⤊ 0⤋
Say x = the number of dogs
then 4x = the number of ducks
A dog has four legs so the number of dogs legs is 4 times the number of dogs = 4 times x = 4x
A duck has two legs so the number of duck legs is 2 times the number of ducks = 2 times 4x = 8x
The total number of legs = dog legs + duck legs
36 = 4x + 8x
36 = 12x
x = 36/12
x=3
number of dogs = x = 3
number of ducks = 4x = 4(3) = 12
2007-12-04 12:59:07 · answer #3 · answered by ignoramus_the_great 7 · 0⤊ 0⤋
x=dogs y=ducks
x=4y
36=4x+2y
Substitute the 4x
36=4(4y)+2y
36=16y+2y
36=18y
36/18=18y/18
2=y (so the number of ducks is 2)
x=4y
x=4(2)
x=8 (this is the number of dogs)
I'm sorry if you just wanted the equations. There are multiple equations used in this problem, so I had to put all of them and solve. I'm sorry if this isn't what you wanted.
2007-12-04 13:08:02 · answer #4 · answered by Anonymous · 0⤊ 0⤋
you would have
x=dogs
4x=ducks
4x+2[(4x)]=36
4legs*dogs+2legs[ducks(4*dogs)]=36 legs
there are 3 dogs for 12 legs
4 times as many ducks as dogs so 12 ducks = 24 legs
12+24=36
i now that wasnt clear hopefully you can make sense of it
2007-12-04 13:08:14 · answer #5 · answered by DisneyKrayzie 4 · 0⤊ 0⤋
x = # of dogs
4x + 2(4x) = 36
4x + 8x = 36
12x = 36
x = 3
3 dogs and 12 ducks
2007-12-04 12:55:27 · answer #6 · answered by sfroggy5 6 · 0⤊ 0⤋
Dk = duck, Dg = dogs
Dk=4*Dg
Legs = 4*Dg + 2*Dk = 36
Those are your equations
2007-12-04 12:53:14 · answer #7 · answered by gp4rts 7 · 0⤊ 0⤋
ask your teacher!!!!
2007-12-04 12:56:31 · answer #8 · answered by Anonymous · 0⤊ 0⤋