Maths-
General
Easy

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 = 2cross timesno. of 2 leg animals  + 4cross timesno. 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 = 2cross timesno. of 2 leg animals  + 4cross timesno. 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 - 2cross timeseq1 to eliminate x
    We get 2 x plus 4 v minus 2 left parenthesis x plus y right parenthesis equals 172 minus 2 left parenthesis 50 right parenthesis
    not stretchy rightwards double arrow 4 y minus y equals 172 minus 100
    not stretchy rightwards double arrow 3 y equals 72
    ∴ y = 24
    Step 3:- substitute the value of y in eq1 to get the value of x
    x plus y equals 50 not stretchy rightwards double arrow x plus 24 equals 50
    not stretchy rightwards double arrow x equals 50 minus 24
    ∴ x = 26
    ∴The no. of 2 leg animals are 26 and no. of 4 leg animals are 24.

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