Answer: 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
