A farmer notes that in a field full of horses and geese there are 36 heads and 106 feet. How many of each animal are there?

17 horses and 19 geese

Step-by-step explanation:

Let x be the number of horses and y be the number of geese

We know that, horses have four feet and geese have 2 feet

It is given that

x+y=36 (i)

and

4x+2y=106 (ii)

Solve the two equations simultaneously by substitution,

From equation (i)

y=36-x (iii)

Substitute y with 36-x in equation (ii)

4x+2(36-x)=106

4x+72-2x=106

4x-2x=106-72

2x=34

x=17

Then

Substitute x=17 to equation (iii)

y=36-17=19

x=17, y=19

We therefore have 17 horses and 19 geese

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .