This morning, some dragons, horses, and chickens were playing in my backyard. i counted 15 heads, 50 legs, and 4 wings. how many dragons, how many horses, and how many chickens were playing in my backyard? (for your information: any healthy dragon has three heads, four legs, and two wings. feel free to use wikipedia to obtain the information about the number of heads, legs, and wings of the rest of the creatures. oh, and all creatures on my backyard were healthy.)

We are given

number of heads =15

we know that

any healthy dragon has three heads

horse has 1 head

chicken has 1 head

Let's assume

number of dragons is x

number of horses is y

number of chickens is z

so, we will get

first equation:

number of legs =50

any healthy dragon has four legs

chicken has 2 legs

horse has four legs

so, we can get second equation as

we can simplify it

now, we can find third equation

dragon has two wings

horse has no wings

chicken has two wings

so, we will get third equations as

now, we can simplify it

so, we will get system of equations as

now, we can use substitution

We can find for z from third equation

we can plug this in first equation

now, we can solve for y

now, we can plug this z and y into second equation

now, we can solve for x

now, we can find y and z

we can plug x=1

we can plug x=1

Hence ,

number of dragons is 1

number of horses is 11

number of chicken is 1............Answer

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: