Create and solve a linear equation that represents the model, where circles and a square are shown evenly balanced on a balance beam.
A. [tex]x+6=16 ; x=10[/tex]
B. [tex]x=6+10 ; x=16[/tex]
C. [tex]x+6=10 ; x=4[/tex]
D. [tex]x+10=6 ; x=-4[/tex]
Answer (2)
Assume the weight of the square is 'x'.
Set up the equation x + 6 = 16 , representing the balance.
Solve for x by subtracting 6 from both sides: x = 16 − 6 .
The weight of the square is 10 .
Explanation
Problem Analysis Let's analyze the problem. We have a balance beam with circles and a square. We need to find the equation that represents the balance and solve for the weight of the square (x).
Setting up the Equation Let's assume the weight of the square is 'x'. From the options, we can see that the number of circles are represented as numbers. We need to find an equation where the square and some circles are balanced by other circles.
Solving Option A Looking at option A, we have x + 6 = 16 . This means the weight of the square plus 6 circles equals the weight of 16 circles. Solving for x, we subtract 6 from both sides: x = 16 − 6 = 10 .
Analyzing Option B Looking at option B, we have x = 6 + 10 , which simplifies to x = 16 . This equation doesn't represent a balance; it just states that the weight of the square is the sum of 6 and 10.
Solving Option C Looking at option C, we have x + 6 = 10 . This means the weight of the square plus 6 circles equals the weight of 10 circles. Solving for x, we subtract 6 from both sides: x = 10 − 6 = 4 .
Analyzing Option D Looking at option D, we have x + 10 = 6 . This means the weight of the square plus 10 circles equals the weight of 6 circles. Solving for x, we subtract 10 from both sides: x = 6 − 10 = − 4 . Since weight cannot be negative, this option doesn't make sense in the context of the problem.
Final Answer Comparing the solutions, option A, x + 6 = 16 ; x = 10 , seems to be the most reasonable. It represents a balance where the square plus 6 circles equals 16 circles, and the weight of the square is 10.
Examples
Imagine you're using a seesaw. On one side, you have a box (the square) and 6 small balls (circles). On the other side, you have 16 small balls. To balance the seesaw, the weight of the box must be equal to the difference in the number of balls on each side. This problem demonstrates how to find the weight of the box using a linear equation, which is a fundamental concept in balancing weights and understanding simple physics.
The linear equation that models the balance of a square and circles is Option A: x + 6 = 16 ; x = 10 , which shows that the weight of the square is 10. This equation represents a balance condition accurately. Other options do not provide valid balance representations.
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