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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