someone has 22 animals with a total of 56 legs, ducks have 2 legs and cows have 4 legs. how many of each animal does this person have?

Question

can you solve this question for me

Answer 1

This sounds like a problem of writing a system of equations and then solving it.  We'll need to write two equations.

 

The information we have:

Total animals = 22

Types of animals: cows and ducks

 

Total legs = 56

Cows have 4 legs, ducks have two.

 

 

The two kinds of information we have are about the number of animals and the number of legs, so that will be what our two equations are about.

 

First, an equation representing the number of animals.  Let's let C be the number of cows and D be the number of ducks. Then

22 = D + C

because the number of cows plus the number of ducks will equal the total number of animals.

 

 

Next, an equation representing the number of legs:

 

56 = 2D + 4C

 

Again, 56 is the number of legs, 2D will give us the total number of duck legs and 4C will give us the total number of cow legs.

 

So our two equations are 

22 =   D +  C

56 = 2D + 4C

 

 

This system can be solved using either elimination or substitution.  Let me know if you'd like more information about these two methods!