A black puppy weighed 5 ounces at birth and grows at a constant rate of 5 ounces per week. A white puppy weighed 10 ounces at birth and grows at a constant rate of 5 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.
Nice!
Complete the table below with the weight of the white puppy, y, after 3, 5, and 7 weeks. You can solve on paper and then enter your answer on Zearn.
y=10+5x

Weeks (x) Weight in oz (y)
3
5
7
Great job!
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)
3 25
5 35
7 45
Great job!
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 for the weight of the black puppy in ounces, \( y \), after \( x \) weeks, you need to consider its initial weight and its growth rate.

The black puppy's initial weight at birth is 5 ounces, and it grows at a constant rate of 5 ounces per week. Therefore, the equation can be written as:

\[ y = 5 + 5x \]

Summary of the Equations

• Black Puppy: \( y = 5 + 5x \)
• White Puppy: \( y = 10 + 5x \)

Next Steps:

If you would like to find a time when the black puppy and the white puppy will be the same weight, you can set the two equations equal to each other:

\[ 5 + 5x = 10 + 5x \]

When you solve this equation, you will find that the black puppy and the white puppy will never be the same weight because the growth rates are the same and the white puppy started heavier. As a result, the black puppy will remain 5 ounces lighter than the white puppy at all times.