Final answer:
The correct equation to determine the number of weeks it will take for the two gorillas to weigh the same amount is 135 + x = 143 - 4x, which is Option 2. Solving this equation yields x = 1.6 weeks.
Step-by-step explanation:
To determine the number of weeks (x) it will take for a mountain gorilla weighing 135 pounds and gaining 1 pound each week to weigh the same as an eastern gorilla weighing 143 pounds and losing 4 pounds each week, we can set up an equation reflecting their weights over time. The mountain gorilla's weight can be represented as 135 + x, and the eastern gorilla's weight as 143 - 4x. We wish to find the point at which these two expressions are equal, i.e., when the weights of the two gorillas are the same.
By setting these two expressions equal to each other, we get the equation 135 + x = 143 - 4x. This equation corresponds to Option 2. To solve for x, add 4x to both sides to eliminate the x term on the right side and subtract 135 from both sides to isolate terms with x. This results in 5x = 8, and dividing both sides by 5 gives us x = 8/5 or 1.6 weeks.