An animal shelter spends $2.50 per day to care for each cat and $4.00 per day to care for each dog. Camden noticed that the shelter spent $100.50 caring for cats and dogs on Thursday. Camden 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?

13 cats were at the shelter on Thursday.

Step-by-step explanation:

Let x represent the number of cats that were at the shelter on Thursday.

Let y represent the number of dogs that were at the shelter on Thursday.

Camden found a record showing that there were a total of 30 cats and dogs on Thursday. This means that

x + y = 30

The animal shelter spends $2.50 per day to care for each cat and $4.00 per day to care for each dog. Camden noticed that the shelter spent $100.50 caring for cats and dogs on Thursday. This means that

2.5x + 4y = 100.5 - - - - - - - - - - - - 1

Substituting x = 30 - y into equation 1, it becomes

2.5(30 - y) + 4y = 100.5

75 - 2.5y + 4y = 100.5

- 2.5y + 4y = 100.5 - 75

1.5y = 25.5

y = 25.5/1.5

y = 17

x = 30 - y = 30 - 17

x = 13

the infinity sign

step-by-step explanation: