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 thursdaySolution:Let "a" denote number of catsLet "b" denote number of dogsCost per day for each cat = $ 4.50Cost per day for each dog = $ 8.50Given that Violet found a record showing that there were a total of 30 cats and dogs on ThursdayThus, number of cats + number of dogs = 30a + b = 30  ------ eqn 1Also given that Violet noticed that the shelter spent $219.00 caring for cats and dogs on ThursdayNumber of cats x cost per day for each cat + Number of dogs x cost per day for each dogs = $ 219[tex]a \times 4.50 + b \times 8.50 = 219[/tex]4.5a + 8.50b = 219  ----- eqn 2Multiply first equation by 4.54.5a + 4.5b = 135  ---- eqn 3Subtract eqn 2 from eqn 34.5a + 4.5b = 135(-)4.5a + 8.50b = 219----------------------------------4b = -84b = 21Substitute this y value into the first equationa + b = 30a + 21 = 30a = 9Thus "a" denotes number of cats, so number of cats on thursday = 9