Question

There are 30 head and 86 leg. How many cow and chicken are there???

Answer 1

We know (assume) that each cow and chicken has one head.
Chickens have 2 legs and cows have 4 legs.

If there are C cows, then there are 30-C chickens.

Count total number of legs
4C+2(30-C) = 86
Simplify and solve for C
4C-2C=86-60
2C=26
C=13
So there are 13 cows and 17 chickens.

Check: 13*4+17*2 = 52+34 = 86 legs...good.

Note: you can also set up a system of equations with two equations and two unknowns if you enjoy solving system of equations.

Answer 2

If all 30 heads are chickens, then there are 60 legs. But we have 86 legs, so there are 26 extra legs.

If we replace a chicken with a cow, we get 2 more legs. We need 26 more legs, requiring 13 cows.

So, there are 13 cows and only 17 chickens.