Question

The weight of keiko's kitten is 1/6 the weight of her puppy. If each animal gains 3 pounds, the kitten will weigh 1/3 as much as the puppy. The equation 1/6w + 3 = 1/3(w + 3) describes this situation, where w is the weight of the puppy now. How much does the puppy weigh now?

Answer 1

The puppy weighs 6 pounds now.

Step-by-step explanation:

To find the weight of the puppy now, we need to solve the equation 1/6w + 3 = 1/3(w + 3) for w.

1. First, let's distribute the 1/3 by multiplying it with w + 3. This gives us 1/6w + 3 = 1/3w + 1.
2. Next, let's combine like terms. Subtracting 1/6w from both sides of the equation gives us 3 = 1/3w - 1/6w + 1.
3. Simplifying the right side of the equation further, we get 3 = 1/6w + 1/6w + 1.
4. Combining like terms again, we have 3 = 2/6w + 1.
5. To get rid of the fraction, we can multiply both sides of the equation by 6. This gives us 18 = 2w + 6.
6. Finally, to isolate w, we can subtract 6 from both sides of the equation. This gives us 12 = 2w.
7. Dividing both sides by 2, we find that w = 6. Therefore, the puppy weighs 6 pounds now.