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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?

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.
Nice!
Complete the table below with the weight of the black puppy, y, after various numbers of weeks, x. You can solve on paper and then enter your answer on Zearn.
y=12+4x

Weeks (x) Weight in oz (y)
1
3
7

1 answer

Let's start by noting the equations of the weights of both puppies after \( x \) weeks.

  1. Weight Equation for the White Puppy: \[ y = 8 + 4x \]

  2. Weight Equation for the Black Puppy: \[ y = 12 + 4x \]

Now, we can fill in the table for the black puppy's weight after various weeks.

Completing the Table for the Black Puppy:

  1. At \( x = 1 \): \[ y = 12 + 4(1) = 12 + 4 = 16 \]

  2. At \( x = 3 \): \[ y = 12 + 4(3) = 12 + 12 = 24 \]

  3. At \( x = 7 \): \[ y = 12 + 4(7) = 12 + 28 = 40 \]

Weights of the Black Puppy:

Weeks (x) | Weight in oz (y) --- | --- 1 | 16 3 | 24 7 | 40

Summary of Weights:

  • After 1 week, the black puppy weighs 16 ounces.
  • After 3 weeks, the black puppy weighs 24 ounces.
  • After 7 weeks, the black puppy weighs 40 ounces.

Finding When They Are the Same Weight:

Both puppies grow at the same rate (4 ounces per week). We can set their equations equal to find out when they will have the same weight:

\[ 12 + 4x = 8 + 4x \]

Subtract \( 4x \) from both sides:

\[ 12 = 8 \]

This results in a contradiction, meaning that the two puppies will never weigh the same amount. The black puppy starts heavier and continues to grow at the same rate, so it will always remain heavier than the white puppy.