Question

a pet store has 30 animals. some are cats the rest are dogs. the cats cost $50 each. the dogs cost $100 each. if the total for all 30 animals is $1900, how many cats are there?

Answer 1

Dogs= X
Cats= Y

X + Y = 30

100x + 50y= 1900

Easiest way is to solve by substitution.

[Looking for Y]

x+y=30

[subtract Y]

X= 30- Y

—————

Next, plug that into the next equation.

100 (30-y) + 50y= 1900

[Distribute]

300- 100y + 50y= 1900

[Combine Like Terms]

300- 50y= 1900

[subtract 300]

-50y= 1600

[divide by -50]

Y= ANSWER

This is Systems of Equations.

Answer 2

There are 22 cats and 8 dogs.

Explanation:

Let the cats be represented by = c

Let the dogs be represented by = d

Given, that the pet store has 30 pets.

First equation forms :

`c+d=30` ........(1)

Also given, the cats cost $50 each and dogs cost $100 each and the total for all is $1900. Now second equation forms:

`50c+100d=1900` .........(2)

From equation (1) we get
`c=30-d`

Putting this value of c in equation 2:

`50(30-d)+100d=1900`

`1500-50d+100d=1900`

=>
`50d=400`

=>
`d=8`

Now,
`c+d=30`

So,
`c=30-8`

`c=22`

Hence, there are 22 cats and 8 dogs.