Question

In the yard were chickens and rabbits. Together they had 28 heads and 78 legs. How many chickens and how many rabbits was in the yard? please explain step by step​

Answer 1

Given:

28 heads and 78 legs

To Find:

Number of chickens and Rabbits

Explanation:

A chicken has 1 head and 2 legs

A rabbit has 1 head and 4 legs

There are 2 methods to solve this type of problem:

1) Algebraic Method

2) Mathematical heuristic called "Assumption Method"

Here, I will present the solution for the more widely known method, the algebraic method.

Solution:

Define x:

Let the number of rabbits be x

The number of chicken will be (28 - x)

Solve x:

There are 78 legs altogether

4x + 2(28 - x) = 78

4x + 56 - 2x = 78

2x = 22

x = 11

Find the number of chickens and rabbits:

Rabbit = x

Rabbit = 11

Chicken = 28 - x

Chicken = 28 - 11

Chicken = 17

Answer: There are 11 rabbits and 17 chickens

Check:

11 rabbits with 4 legs each

17 chickens with 2 legs each

11 + 17 = 28 heads

11 x 4 + 17 x 2 = 78 legs

Answer 2

Answer:

there are 11 rabbits and 17 chickens