in a farm, there are some goats and some ducks. if the animals have a total of 15 heads and 44 legs, how many goats are there

Question

hard math

Answer 1

Hi Jesse,

Hopefully each of the animals has one head :) What we can do to set this up is assign a variable for goats, let's use G, and assign a variable for ducks, let's use D. We can first say that:

G + D = 15

They also tell us that there are 44 legs. We know that there are 4 legs on a goat and 2 legs on a duck. So we can say that the total number of legs can be represented by this equation:

4G + 2D = 44

Now, we have a system of equations!

If we were to solve for one of the variables first, we can substitute to solve for the other one!

Let's say we want to solve for G (number of goats) first. That means we would want to know what D is equivalent to in terms of G.

If we take G + D = 15, and rearrange it algebraically and subtract G on both sides, we know that

D = -G + 15

If we substitute -G + 15 for D into the other equation 4G + 2D = 44, we would get....

4G + 2(-G+15) = 44 (Algebraically solve for G)

4G - 2G + 30 = 44

2G = 14

G = 7

Therefore, we have 7 goats! Since we have 15 total animals, there are 8 ducks.

Let me know if you have any questions.

Thanks!