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 
cost of each cat ( The cats cost $50 each)
cost of x cats = 50x (in $ )
cost of y dogs = y cost 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 eq1 to eliminate x
We get 50x + 100y - 50(x + y) = 1,900 - 50(30)
∴ y = 8
Step 3:- substitute the value of y in eq1 to get the value of x
∴ x = 22
∴ The animals shop has 22 cats and 8 dogs in total of 30 animals.
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