Question

In a forest you observed 22 eyes and 32 legs belonging to owls and foxes. a) How many owls and how many foxes are there? b) If on another day you saw 24 eyes and 38 legs, how many foxes and how many owls are there?​

Answer 1

a) Let's say the number of owls is "x" and the number of foxes is "y".

Each owl has 2 eyes and 2 legs, so "x" owls would have 2x eyes and 2x legs.

Each fox has 2 eyes and 4 legs, so "y" foxes would have 2y eyes and 4y legs.

According to the problem, there are 22 eyes and 32 legs in total:

2x + 2y = 22 (equation 1)

2x + 4y = 32 (equation 2)

We can use these two equations to solve for "x" and "y".

Subtracting equation 1 from equation 2:

2x + 4y - (2x + 2y) = 32 - 22

2y = 10

y = 5

Substituting "y" = 5 into equation 1:

2x + 2(5) = 22

2x = 12

x = 6

Therefore, there are 6 owls and 5 foxes.

b) Let's use the same approach to solve for "x" and "y":

2x + 2y = 24 (equation 1')

2x + 4y = 38 (equation 2')

Subtracting equation 1' from equation 2':

2x + 4y - (2x + 2y) = 38 - 24

2y = 14

y = 7

Substituting "y" = 7 into equation 1':

2x + 2(7) = 24

2x = 10

x = 5

Therefore, there are 5 owls and 7 foxes.