There are 23 animals in the field. Some are pigs and some are ducks. There are 80 legs in all. How many of each animal are in the field?

Question

asked Oct 19, 2023 228k views

1 Answer

Ingo Radatz · Answer 1 · 2023-10-23T05:58:09+0000

Answer:

Pigs = 17

Ducks = 6

Explanation:

Let there be x pigs and y ducks in the field.

$\implies x + y =23$

$\implies y =23-x.....(1)$

Since, there are 80 legs in all.

Each pig has 4 legs and each duck has 2 legs. So, x pigs will have 4x legs and y ducks will have 2y legs.

Total legs = 4x + 2y

Total legs = 80 (Given)

$\implies 4x + 2y =80....(2)$

From equations (1) & (2), we find:

$\implies 4x + 2(23-x) =80$

$\implies 4x + 46-2x =80$

$\implies 2x =80-46$

$\implies 2x =34$

$\implies x =(34)/(2)$

$\implies x =17$

$\implies y =23-17$

$\implies y =6$