Final answer:
The left scale would measure 605 pounds when a 600-pound weight is placed on a 10-pound board, 2/3 closer to the left scale than to the right scale, as this is a simple fulcrum problem where weight is distributed based on the lever arm principle.
Step-by-step explanation:
To solve how much the left scale would measure when a 600-pound weight is placed on a 10-pound board, 2/3 closer to the left side than to the right side, you should imagine this scenario as a simple fulcrum problem. Imagine the fulcrum, which is the balancing point, is at the center of the board. The total weight of the board (10 pounds) can be considered as equally distributed between the two sides. However, the 600-pound weight is not centered.
As the weight is 2/3 closer to the left, you can divide the board into three equal parts (each part representing 1/3 of the board's length). The weight is then effectively acting on the first part, which is the side closer to the left scale. Since the right side is balancing the same weight at a longer lever arm, we need to find the balance point or the 'moment' each side is exerting around the fulcrum.
To solve for the left scale, the following equation can be used: Weight_left x Distance_left = Weight_right x Distance_right. For the left scale, we can assume Distance_left to be 1 unit since the weight is right above it, making the equation much simpler. The total weight is 600 pounds plus half the board's weight (5 pounds), as the other half would be on the other side. Thus, the left scale will bear the weight of 605 pounds times its distance (1 unit) from the fulcrum.
The right scale will then take up the remainder of the total weight to balance it out. To find the amount on the left scale, we can set up a proportion considering that on one side we have 2/3 of the distance from the fulcrum (left side) and on the other side 1/3 of the distance (right side). The proportion would be 605 pounds / X pounds = 1/3 / 2/3, leading to X being twice the weight on the left scale. Solving this gives us X = 605 pounds * (2/3 / 1/3) = 605 pounds * 2 = 1210 pounds. But we need to remember that the weight is distributed, so the left scale will only bear half of this X, which is 605 pounds.