Four balances are shown where the two sides of each contain exactly the same amount of weight. The first balance has 4 squares, 1 triangle and 1 ball on the left side, right side has 2 diamonds. The second balance has 1 triangle and 1 square on the left side, 1 ball on the right side. The third balance has 1 triangle and 1 diamond on the left side, 1 ball and 2 squares on the right side. The fourth triangle has 1 diamond, 1 triangle and 1 square on the left side. How many balls are on the right side? Explain/show how this was determined.
see earlier post, check it carefully.
The total surface area if 3dfigure
The total surface area if 3D figure
The total surface area of 3D figure
To determine the number of balls on the right side, we need to analyze each balance and compare the weights on both sides. Let's go through each balance step-by-step:
1. Balance 1: On the left side, we have 4 squares, 1 triangle, and 1 ball. On the right side, we have 2 diamonds. Since both sides of the balance are equal in weight, we can conclude that the weight of the 4 squares, 1 triangle, and 1 ball is equal to the weight of the 2 diamonds. However, we cannot identify the weight of the individual objects from this balance alone.
2. Balance 2: On the left side, we have 1 triangle and 1 square. On the right side, we have 1 ball. Again, since both sides are equal in weight, we can conclude that the weight of the triangle and square is equal to the weight of the ball. However, we still cannot determine the weight of the individual objects.
3. Balance 3: On the left side, we have 1 triangle and 1 diamond. On the right side, we have 1 ball and 2 squares. Once again, the two sides are equal in weight. This tells us that the combined weight of the triangle and diamond is the same as the combined weight of the ball and the two squares.
4. Balance 4: On the left side, we have 1 diamond, 1 triangle, and 1 square. Since we are only asked to determine the number of balls on the right side, we don't need to consider this balance further.
Now, let's combine the information from the first three balances to determine the number of balls on the right side. We'll compare the weights indirectly by using the equalities we derived:
From Balance 3: triangle + diamond = ball + 2 squares (1)
From Balance 2: triangle + square = ball (2)
From Balance 1: 4 squares + triangle + ball = 2 diamonds (3)
Since we want to determine the number of balls, we'll focus on equations (1) and (2) to eliminate the other variables.
From equation (1), we rearrange it to: ball = triangle + diamond - 2 squares (4)
Now we substitute this expression for "ball" in equation (2):
triangle + square = triangle + diamond - 2 squares
Simplifying, we get:
0 = diamond - 3 squares (5)
Now, combining equation (3) and equation (5), we can solve for the number of balls:
4 squares + triangle + ball = 2 diamonds
4 squares + triangle + (triangle + diamond - 2 squares) = 2 diamonds
Simplifying, we get:
2 squares + 2 triangle = diamond
Since we know that the diamond count equals the ball, we can conclude that:
2 squares + 2 triangle = ball
Therefore, there are 2 squares and 2 triangles on the right side, or equivalently, 1 ball.
Hence, the answer is that there is 1 ball on the right side.