Final answer:
Abe's dog and Sam's dog will weigh the same after 3 weeks. The equation 2(x + 3) = 3(x + 1) was solved to find that x equals 3 when both weights are equal.
Step-by-step explanation:
The question asks when the weight of Abe's dog, which is calculated as 2(x + 3), will be the same as the weight of Sam's dog, which is given by 3(x + 1), with x representing the number of weeks. To solve for x when both weights are equal, we need to set the two expressions equal to each other and solve the resulting equation:
2(x + 3) = 3(x + 1)
Distribute the numbers outside the parentheses:
2x + 6 = 3x + 3
Now, subtract 2x from both sides:
6 = x + 3
Lastly, subtract 3 from both sides to solve for x:
x = 3
Thus, after 3 weeks, both dogs will weigh the same.