Question

# 50 animals are there in a shed. Some of the animals have 2 legs and the rest of them have 4 legs. In total there are 172 legs. Frame the system of linear equations and use elimination method to solve .

Hint:

### let the no. of 2 leg animals be x and let the number of 4 leg animals be y

Given total no. of animals = no. of 2 leg animals + no. of 4 leg animals = 50

Given no. of legs = 2no. of 2 leg animals + 4no. of 4 leg animals = 172.

## The correct answer is: 24

### Ans :- The no. of 2 leg animals are 26 and no. of 4 leg animals are 24.

Explanation :-

Step 1:- Frame the equations

let the no. of 2 leg animals be x and let the number of 4 leg animals be y

Given total no. of animals = no. of 2 leg animals + no. of 4 leg animals = 50

i. e x + y = 50 — eq1

Given no. of legs = 2no. of 2 leg animals + 4no. of 4 leg animals = 172.

i. e 2x+4y = 172 — eq2

So the equations are x + y = 50 and 2x + 4y = 172

Step 2 :- eliminate x to find value of y

Doing eq2 - 2eq1 to eliminate x

We get

∴ y = 24

Step 3:- substitute the value of y in eq1 to get the value of x

∴ x = 26

∴The no. of 2 leg animals are 26 and no. of 4 leg animals are 24.

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