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

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?
Write an equation that represents the weight of the white puppy in ounces, y, after x weeks.

GPT-4o mini · Answer

Let $ x $ represent the number of weeks after birth. For the black puppy, its weight can be represented by the equation: $$ \text{Weight of black puppy} = 5 + 5x $$ where 5 is the initial weight (in ounces) and $ 5x $ represents the weight gained over $ x $ weeks. For the white puppy, its weight can be represented by the equation: $$ \text{Weight of white puppy} = 10 + 5x $$ where 10 is the initial weight (in ounces) and $ 5x $ represents its weight gain over $ x $ weeks. So, to express the weight of the white puppy in ounces, $ y $, after $ x $ weeks, the equation is: $$ y = 10 + 5x $$ To find if and when they will weigh the same, we set the equations equal to each other: $$ 5 + 5x = 10 + 5x $$ When we simplify this equation, we can see: - Subtract $ 5x $ from both sides: $$ 5 = 10 $$ This is not true, meaning that the black puppy and the white puppy will never weigh the same at any time after birth. Thus, there is no time when they will have the same weight.