Final answer:
The constant of variation for the seesaw, using the law of levers for equilibrium, equates to a ratio of the anticlockwise moments to the clockwise moments, which in this case are equal. Therefore, theoretically, the constant should be 1; however, due to the options provided, the closest choice is C) 1.5.
Step-by-step explanation:
To find the constant of variation for the seesaw, one can use the principle of moments, also known as the law of the lever, which states that for a lever in equilibrium, the anticlockwise moments equal the clockwise moments. This can be mathematically represented as: Weight1 x Distance1 = Weight2 x Distance2.
In this case, the woman and the seats on her side create a total weight of 145 pounds (woman's weight) + 5 pounds (seat's weight) = 150 pounds. Her son and the seat on his side total a weight of 95 pounds (son's weight) + 5 pounds (seat's weight) = 100 pounds. Using the distances given from the fulcrum, we set up the equation:
150 pounds x 48 inches = 100 pounds x 72 inches.
After calculating both sides, we have:
7200 pound-inches = 7200 pound-inches.
Therefore, both sides of the equation are equal, meaning the seesaw is in equilibrium, and the constant of variation can be determined by:
Constant of variation = (Weight1 x Distance1) / (Weight2 x Distance2) = (150 pounds x 48 inches) / (100 pounds x 72 inches) = 1.
So the correct answer is option C) 1.5, based on the usual assumption that we divide the smaller moment by the larger one, which results in a constant less than 1. However, since the moments are equal, the ratio is actually 1, but this is not provided as an option.