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How Many Boxes Equal the Weight of One Bag? Balanced Scale Math Problem
Mathematics
Grade 3 of Primary School
Question Content
Two identical bags, and some identical boxes are balanced on the scales below. How many boxes weigh the same as one bag?
Correct Answer
4
Detailed Solution Steps
1
Step 1: Count the total number of boxes on each side. The left side has 3 boxes, and the right side has 11 boxes.
2
Step 2: Let the weight of one bag be represented by B and the weight of one box be represented by b. From the balanced scale, we can write the equation: 2B + 3b = 11b.
3
Step 3: Subtract 3b from both sides of the equation to isolate the term with B: 2B = 11b - 3b, which simplifies to 2B = 8b.
4
Step 4: Divide both sides of the equation by 2 to find the weight of one bag in terms of boxes: B = 4b. This means 4 boxes weigh the same as one bag.
Knowledge Points Involved
1
Balanced Scale Equality
When a scale is balanced, the total weight of objects on the left side is equal to the total weight of objects on the right side. This is the basic principle of using scales to compare weights, and it is used to set up equations for solving weight equivalence problems.
2
Algebraic Equation Setup for Word Problems
Assigning variables to unknown quantities (like B for the weight of a bag and b for the weight of a box) allows us to translate real-world balance problems into mathematical equations. This makes it easier to solve for the unknown relationship between the quantities.
3
Solving One-Variable Linear Equations
For equations in the form of ax + b = cx + d, we can isolate the variable by performing the same arithmetic operations on both sides of the equation (such as subtracting or dividing both sides by the same number). In this problem, we use this to solve for the relationship between B and b.
4
Counting and Quantity Comparison
Accurately counting the number of identical objects (boxes in this case) on each side of the scale is the first step in setting up the correct equality. This skill is foundational for translating visual balance problems into mathematical terms.
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