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Oksana_A [137]
3 years ago
14

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 shel

ter 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?
Mathematics
1 answer:
svp [43]3 years ago
3 0

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

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factors of 50: 1,2,5,10,25,50

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y = 1 - 50/1
y = 1 - 50
y = -49
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do the same for the rest and get
(2, -24)
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