Question

there are 30 legs in my backyard, but I'm counting dogs and kids. How many kids and dogs are in my backyard?

Answer 1

Well, we know:
\[
2n+4k=30\implies\\
n+2k=15
\]To find an integral solution, we use Bézout's identity and the Extended Euclidean Algorithm (or just common sense) to find that there are multiple positive solutions to the problem. A few of them:
\[n=1, k=7\\
n=3,k=6\\
n=5,k=5\]Et al. These are represented as, for some integer \(l\):
\[
n=1+2l\\
k=7-l
\]

Answer 2

my lil sister needs help is there by any chance u can explain it a little easy way?

Answer 3

she is in grade 4

Answer 4

Sure, I guess. So we have the number of legs of a dog is four, while the number of legs on children is two. If we know the amount of dogs, we multiply it by four to get the amount of legs from dogs, same with the children, right? So, look for the number of dogs and children such that their legs add up to the correct value.

Answer 5

can u show me by step llol

Answer 6

All right, so, let's say we have a number of dogs \(d\), and we have a number of kids \(k\). WE know a dog has four legs, so, we multiply the number of dogs by 4, to get how many legs there are, so:
\(4d=\) number of dog's legs.
And we know that kids have two legs, so:
\(2k=\) number of kid's legs.
Now we know these must add up to thirty, since we have that the number of legs is 30, so:
\(4d+2k=30\) total legs.
Try some number of dogs and kids you think is right, to see what you are able to get, such that their total number of legs adds up to thirty.

Answer 7

IS IT LIKE THIS 4D+2K=30
4(5)+2(5)= 30

Answer 8

20 DOG LEGS AND 10 KIDS LEGS

Answer 9

That's one answer, yes.

Answer 10

WHAT DO I DO TO GET THE OTHER ANSWER

Answer 11

Think about this, it might be a little difficult to get your head around, because LDE's (the names for these types of equations) are not easy.
How can you change both numbers to make them add up to the same result? If you do something to one, what must you do to the other to make sure these are always equal?

Answer 12

15 and 15

Answer 13

idk what to do

Answer 14

No, 15 and 15 would not allow the number of legs to add up. Try playing with the numbers... try changing one *without* changing the other (remember, they're separate), and then try to 'fix' the equation by changing the other number, but not the first.

Answer 15

so the first one is correct

Answer 16

20 for dogs

Answer 17

No, the first one is correct. If we have 5 dogs and 5 kids:
\[
5\cdot4+5\cdot2=20+10=30
\]Right? So, try and change the 5 dogs to something else (say 6?) and try to 'fix' the number of legs by changing the number of kids.

Answer 18

6 times 4 = 24
2times 3= 6

Answer 19

is it right????

Answer 20

Refer to the attached solution pdf file.

Answer 21

Yes, that is correct. That is a second solution.