A farmer looks out her window and sees ducks and rabbits. She says to her husband, "I see 36 heads and 80 feet." Assuming she counted correctly, how many ducks did she see

The number of duck is 32.

Step-by-step explanation:

Let x represent the number of rabbits.

Let y represent the number of ducks

From the question given:

The sum of rabbit and duck is 36 i.e

x + y = 36 (1)

The sum of the feets of the rabbit and duck is 80.

Rabbits has 4 legs

Duck has 2 legs

Therefore, the sum their feets (i.e 80) can be written as:

4x + 2y = 80 (2)

The equations are:

x + y = 36 (1)

4x + 2y = 80 (2)

Solving by substitution method:

From equation (1)

x + y = 36

Make x the subject

x + y = 36

x = 36 - y

Substitute the value of x into equation (2)

4x + 2y = 80

x = 36 - y

4(36 - y) + 2y = 80

Clear bracket

144 - 4y + 2y = 80

144 - 2y = 80

Collect like terms

- 2y = 80 - 144

- 2y = - 64

Divide both side by - 2

y = - 64/ - 2

y = 32

Therefore, the number of duck is 32.

let soccer = x and golf = y

part a

1st equation: x + y = 125

2nd equation: x = y +45

part b

replace x in the 1st equation with the 2nd one:

y + 45 + y = 125

simplify:

2y + 45 = 125

subtract 45 from each side:

2y = 80

divide both sides by 2:

y = 80/2

y = 40

she plays golf for 40 minutes.

part c

no because she plays soccer for 45 minutes longer than golf 40 +45 =   85 minutes, not 80 minutes.