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?

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.