Question

Meghan needs to board her cats and dogs at a kennel while she's on vacation. Pet Hotel charges $42.50 for a cat and $64.00 for a dog for a total cost of $277.00. Animal Spa charges $35.50 for a cat and $50.50 for a dog, for a total cost of $222.50. How many cats and how many dogs does Meghan have?

Answer 1

2 Cats and 3 Dogs.

Explanation:

Let the number of cats owned by Megan =c

Let the number of dogs owned by Megan =d

Pet Hotel charges $42.50 for a cat and $64.00 for a dog for a total cost of $277.00.

This gives us:

• 42.50c+64.00d=277.00

Animal Spa charges $35.50 for a cat and $50.50, for a total cost of $222.50.

This gives us:

• 35.50c+50.50d=222.50

We have derived two linear equations which we can now solve simultaneously for c and d.

• 42.50c+64.00d=277.00

• 35.50c+50.50d=222.50

Multiply the first equation by 50.50 and the second equation by 64.

• 2146.25c+3232d=13988.50
• 2272c+3232d=14240

Subtract

• -125.75c=-251.50

Divide both sides by -125.75

• c=2

Substitute c=2 into any of the equations to obtain d.

42.50c+64.00d=277.00

42.50(2)+64.00d=277.00

85+64.00d=277.00

64.00d=277-85=192

Divide both sides by 64

• d=3

Meghan has 2 Cats and 3 Dogs.

Answer 2

3 dogs and 2 cats.

Explanation:

In this case we can solve it using a 2x2 system of equations, like this:

let x: number of cats

let y: number of dogs

So:

42.5 * x + 64 * y = 277

35.5 * x + 50.5 * y = 222.5 => x = (222.5 - 50.5 * y) /35.5

Replacing, we are left with that:

42.5 * (222.5 - 50.5 * y) /35.5 + 64 * y = 277

266.37- 60.45 * y + 64 * y = 277

64 * y - 60.45 * y = 277 - 266.37

3.55 * y = 10.63

y = 10.63 / 3.55

y = 2.99, about 3

Now to calculate x:

x = (222.5 - 50.5 * 3) /35.5

x = 2

Which means that it has a total of 3 dogs and 2 cats.