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?

2 Cats and 3 Dogs.

Step-by-step 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:

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

This gives us:

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

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

Subtract

Divide both sides by -125.75

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

Meghan has 2 Cats and 3 Dogs.

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2