Maths-
General
Easy

Question

A pet store has 30 animals. Some are cats and the rest are dogs. The cats cost $50 each. The dogs cost $100each. If the total cost for all 30 animals is $1900, how many cats are there?

Hint:

let the no. of cats be x and let the no. of dogs  be y
Given total no. of animals   = no. of cats   + no. of dogs  = 30
Given total cost of all animals  = cost of x cats  + cost of y dogs = $1900.

The correct answer is: 22 cats


    Ans :-The animal shop has 22 cats .
    Explanation :-
    Step 1:- construct the system of linear equations
    let the no. of cats be x and let the no. of dogs  be y
    Given total no. of animals   = no. of cats   + no. of dogs  = 30
    So, x + y = 30 — eq1
    Given total cost of all animals  = cost of x cats  + cost of y dogs = $1900.
    cost of x cats = x cross times cost of each cat ( The cats cost $50 each)
    cost of x cats  = 50x (in $ )
    cost of y dogs = y cross timescost of each dog ( The dogs cost $100each)
    cost of y dogs  = 100y (in $)
    So total cost of all animals = 50x + 100y = 1.900 — eq2
    Step 2 :- eliminate x to find value of y
    Doing  eq2 - 150 cross timeseq1 to eliminate x
    We get 50x + 100y - 50(x + y) = 1,900 - 50(30)
    not stretchy rightwards double arrow 100 y minus 50 y equals 1 comma 900 minus 1 comma 500
    not stretchy rightwards double arrow 50 y equals 400 not stretchy rightwards double arrow y equals 8
    ∴ y = 8
    Step 3:- substitute the value of y in eq1 to get the value of x
    x plus y equals 30 not stretchy rightwards double arrow x plus 8 equals 30
    not stretchy rightwards double arrow x equals 30 minus 8
    ∴ x = 22
    ∴ The animals shop has 22 cats and 8 dogs in total of 30 animals.

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