To find the equation that represents the weight of the white puppy in ounces, \(y\), after \(x\) weeks, we can start with the information given in the problem.
The white puppy weighed 12 ounces at birth and grows at a constant rate of 3 ounces per week. Therefore, its weight after \(x\) weeks can be represented by the equation:
\[ y = 12 + 3x \]
where:
- \(y\) is the weight of the white puppy after \(x\) weeks,
- 12 is the initial weight of the white puppy at birth,
- 3 is the growth rate in ounces per week, and
- \(x\) is the time in weeks.
Now, if you're also interested in when the black puppy and the white puppy might weigh the same, we can derive the equation for the black puppy as well.
The black puppy starts at 6 ounces and also grows at a constant rate of 3 ounces per week, which gives us the equation:
\[ y = 6 + 3x \]
To find the time when both puppies weigh the same, we can set the two equations equal to each other:
\[ 6 + 3x = 12 + 3x \]
Solving this equation, we see that the \(3x\) terms cancel out, which leads to:
\[ 6 = 12 \]
Since this statement is false, we can conclude that the black puppy and the white puppy will never weigh the same.
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