A black puppy weighed 12 ounces at birth and grows at a constant rate of 4 ounces per week. A white puppy weighed 8 ounces at birth and grows at a constant rate of 4 ounces per week. Is there a time when they will be the same weight?

Question

Write an equation that represents the weight of the white puppy in ounces, y, after x weeks.
Excellent!
Complete the table below with the weight of the white puppy, y, after 4, 6, and 8 weeks. You can solve on paper and then enter your answer on Zearn.
y=8+4x

Weeks (x) Weight in oz (y)
4
6
8
You got it!
Next, graph the points you just found on the coordinate plane to show the relationship between x, the number of weeks, and y, the weight in ounces of the white puppy.
Weeks (x) Weight in oz (y)
4 24
6 32
8 40
You got it!
Now, consider the black puppy. Write an equation that represents the weight of the black puppy in ounces, y, after x weeks.

Answer 1

To write an equation that represents the weight of the black puppy in ounces, \( y \), after \( x \) weeks, you start with its initial weight of 12 ounces at birth and add its growth rate of 4 ounces per week. The equation is:

\[ y = 12 + 4x \]

Now, to find the weights after a set number of weeks (4, 6, and 8 weeks), you can substitute \( x \) with those values.

Calculating the weights of the black puppy:

1. After 4 weeks: \[ y = 12 + 4(4) = 12 + 16 = 28 \text{ ounces} \]

2. After 6 weeks: \[ y = 12 + 4(6) = 12 + 24 = 36 \text{ ounces} \]

3. After 8 weeks: \[ y = 12 + 4(8) = 12 + 32 = 44 \text{ ounces} \]

Now, here's the completed table with the weight of the black puppy:

| Weeks (x) | Weight in oz (y) | |-----------|-------------------| | 4 | 28 | | 6 | 36 | | 8 | 44 |

So, the weights of the black puppy after 4, 6, and 8 weeks are 28 ounces, 36 ounces, and 44 ounces, respectively.