Help With Word Problem(Elimination)

Question

An animal shelter spends $2.50 per day to care for each cat and $5.00 per day to care for each dog. Evan noticed that the shelter spent $62.50 caring for cats and dogs on Tuesday. Evan found a record showing that there were a total of 23 cats and dogs on Tuesday. How many cats were at the shelter on Tuesday?

Answer 1

Hi Jay, let C represent the cats and D represent the dogs. We can create two equations to represent the information given.

 

Equation 1:

 

The number of cats, C, plus the number of dogs, D, equals the total number of cats and dogs, 23.

 

C + D = 23

 

Equation 2:

 

Cost of maintaining the cats and dogs. It costs $2.50 to maintain one cat. It costs $5.00 to maintain one dog. The shelter spent $62.50 to maintain the cats and dogs.

 

2.50 * C + 5.00 * D = 62.50

 

I do not like to work with decimals, so multiply each term by 100:

 

250C + 500D = 6250

 

The two equations together:

 

      C  +      D  =   23

250C  + 500D = 6250 

 

Multiply the first equation by -500:

 

-500C  - 500D = -11500

 250C + 500D =    6250

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

-250C             =  -5250

 

Divide both sides by -250:

 

C = 21

 

Substitute for C in the first equation:

 

D + 21 = 23

 

Subtract 21 from both sides:

 

D = 2

 

The shelter cared for 21 cats and 2 dogs on Tuesday.

 

Questions?