James's Dog, Buddy, is 2 years older than Fluffy, the neighbor's cat. Three Years ago, Buddy was three times older than fluffy. How old are the dog and cat now?

The required age of the dog buddy is 6 years old and the age of cat fluffy is 4 years old.

Given ,

James's dog buddy is 2 years older than Fluffy,

And the neighbor's cat Three Years ago, Buddy was three times older than fluffy.

Let ,

The age of buddy = B

The age of fluffy is = F

According to the question ,

Buddy, is 2 years older than Fluffy= Age of Buddy = Age of fluffy + 2 years older.

B = F +2

Again According to the question,

Three years ago age of Buddy = B - 3

Three years ago age of Fluffy = F - 3

Three years ago Buddy was three times older than fluffy = Three years ago age of Buddy = 3 × Three years ago Age of fluffy

B - 3 = 3 ( F - 3 )

Solving the equations,

B - 3 = 3 ( F - 3 )

Put the value of B from equation 1

F + 2 - 3 = 3 ( F -3 )

F - 1 = 3F - 9

F - 3F = - 9 +1

-2F = -8

2F = 8

F = 4

The age of fluffy is 4 years old.

Then ,

The age of buddy

B = F + 2

B = 4 + 2

B = 6

The age of buddy is 6 years old.

The required age of the dog buddy is 6 years old and the age of cat fluffy is 4 years old.

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The cat is 4 years old, and the dog is 6 years old.

Step-by-step explanation:

We know that Buddy is 2 years old than Fluffy.

And 3 years ago, Buddy was 3 times older than Fluffy.

Let's define the variables:

B = age of Buddy

F = age of Fluffy.

The first statement can be written as:

B = F + 2

The second statement can be written as:

B - 3 = 3*(F - 3)

To solve this, we can replace the first equation into the second one, and solve that for F

B - 3 = 3*(F - 3)

(F + 2) - 3 = 3*F - 9

F - 1 = 3*F - 9

-1 + 9 = 3*F - F

8 = 2*F

8/2 = 4 = F

Fluffy is 4 years old, and with the first equation we can find the age of Buddy.

B = F + 2 = 4 + 2 = 6

Buddy is 6 years old

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