contestada

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.)

Respuesta :

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:

[tex] 3x+y+z=15 [/tex]

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

[tex] 4x+4y+2z=50 [/tex]

we can simplify it

[tex] 2(2x+2y+z)=50 [/tex]

[tex] 2x+2y+z=25 [/tex]

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

[tex] 2x+0y+2z=4 [/tex]

now, we can simplify it

[tex] 2x+2z=4 [/tex]

[tex] 2(x+z)=4 [/tex]

[tex] x+z=2 [/tex]

so, we will get system of equations as

[tex] 3x+y+z=15 [/tex]

[tex] 2x+2y+z=25 [/tex]

[tex] x+z=2 [/tex]

now, we can use substitution

We can find for z from third equation

[tex] z=2-x [/tex]

we can plug this in first equation

[tex] 3x+y+2-x=15 [/tex]

now, we can solve for y

[tex] 2x+y+2=15 [/tex]

[tex] y=13-2x [/tex]

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

[tex] 2x+2(13-2x)+2-x=25 [/tex]

now, we can solve for x

[tex] x-4x+26=23 [/tex]

[tex] -3x=-3 [/tex]

[tex] x=1 [/tex]

now, we can find y and z

[tex] y=13-2x [/tex]

we can plug x=1

[tex] y=13-2*1 [/tex]

[tex] y=11 [/tex]

[tex] z=2-x [/tex]

we can plug x=1

[tex] z=2-1 [/tex]

[tex] z=1 [/tex]

Hence ,

number of dragons is 1

number of horses is 11

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

Otras preguntas