There are 30 head and 86 leg. How many cow and chicken are there???
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.
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.
To determine the number of cows and chickens given the number of heads and legs, we need to set up a system of equations.
Let's assume that the number of cows is represented by 'c' and the number of chickens is represented by 'h'.
Now, we can set up two equations based on the given information:
1) Equation for the number of heads: c + h = 30
2) Equation for the number of legs: 4c + 2h = 86
We have two equations and two variables, so we can solve this system of equations.
To do this, we can use a common method called substitution or elimination.
Let's solve it using substitution:
From the first equation, we can isolate one variable:
c = 30 - h
Now substitute this value in the second equation:
4(30 - h) + 2h = 86
120 - 4h + 2h = 86
-2h = 86 - 120
-2h = -34
Divide both sides by -2 to solve for h:
h = -34 / -2
h = 17
Now substitute the value of h back into one of the original equations:
c + 17 = 30
c = 30 - 17
c = 13
So, there are 13 cows and 17 chickens.