An animal shelter spends $4.50 per day to care for each cat and $8.50 per day to care for each dog. violet noticed that the shelter spent $219.00 caring for cats and dogs on thursday. violet found a record showing that there were a total of 30 cats and dogs on thursday. how many cats were at the shelter on thursday?

There were 9 cats on the shelter on thursday

Solution:

Let "a" denote number of cats

Let "b" denote number of dogs

Cost per day for each cat = $ 4.50

Cost per day for each dog = $ 8.50

Given that Violet found a record showing that there were a total of 30 cats and dogs on Thursday

Thus, number of cats + number of dogs = 30

a + b = 30  ------ eqn 1

Also given that Violet noticed that the shelter spent $219.00 caring for cats and dogs on Thursday

Number of cats x cost per day for each cat + Number of dogs x cost per day for each dogs = $ 219

4.5a + 8.50b = 219  ----- eqn 2

Multiply first equation by 4.5

4.5a + 4.5b = 135  ---- eqn 3

Subtract eqn 2 from eqn 3

4.5a + 4.5b = 135

(-)4.5a + 8.50b = 219

---------------------------------

-4b = -84

b = 21

Substitute this y value into the first equation

a + b = 30

a + 21 = 30

a = 9

Thus "a" denotes number of cats, so number of cats on thursday = 9

the answer is 13/48

step-by-step explanation: