Question

At a local pet store, there are a total of 7 cats and dogs available for adoption. There is one more than twice as many dogs as cats. If x represents the number of cats and y represents the number of dogs, how many cats and dogs are available for adoption at the pet store?

a) 2 cats and 3 dogs
b) 3 cats and 4 dogs
c) 4 cats and 3 dogs
d) 5 cats and 6 dogs

Answer 1

To solve the problem, set up a system of equations using x and y to represent the number of cats and dogs. Solve the system of equations using either substitution or elimination method. The solution is 2 cats and 5 dogs, so the correct answer is d) 5 cats and 6 dogs.

Step-by-step explanation:

To solve this problem, we can set up a system of equations using the given information. Let's use x to represent the number of cats and y to represent the number of dogs. Based on the information given, we can create two equations:

1. y = 2x + 1 (There is one more than twice as many dogs as cats.)
2. x + y = 7 (There are a total of 7 cats and dogs available for adoption.)

We can solve this system of equations by substitution or elimination. Let's use substitution to solve for x:

1. Substitute y in the second equation with 2x + 1 from the first equation: x + (2x + 1) = 7
2. Simplify the equation: 3x + 1 = 7
3. Subtract 1 from both sides: 3x = 6
4. Divide both sides by 3: x = 2

Now that we know x = 2, we can substitute it back into the first equation to find y:

1. y = 2(2) + 1
2. y = 4 + 1
3. y = 5

Therefore, there are 2 cats and 5 dogs available for adoption at the pet store. The correct answer is option d) 5 cats and 6 dogs.