Question

In a field there are cows, birds, and spiders. Spiders have 4 eyes and 8 legs each. In the field there are 20 eyes and 30 legs. All three animals are present, and there is an odd number of each animal. How many spiders, cows, and birds are present?

Answer 1

Answer:

1 spider, 3 cows, 5 birds.

Step-by-step explanation:

Cows (C): 4 legs, 2 eyes.

Birds (B): 2 legs, 2 eyes.

Spiders (S): 8 legs, 4 eyes.

The number of legs and eyes are given, respectively by:

$30 = 4C+2B+8S\\20 = 2C+2B+4S$

Multiplying the second equation by -2 and adding it to the first one gives us the number of birds:

$30 -40= 4C-4C+2B-4B+8S-8S\\-10 = -2B\\B=5$

Rewriting the original equations with B =5:

$30 = 4C+2*5+8S\\20 = 2C+2*5+4S\\20 = 4C+8S\\10 = 2C+4S\\C=5-2S$

Since the number of cows cannot be negative, and both C and S must be odd numbers, the only possible value of S is 1:

$C=5-2S\\S=1\\C=3$