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Finding the Third Proportional to 82,410 and 180,858

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Solution

The third proportional to 82,410 and 180,858 is: 396,913.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,410 : 180,858 = 180,858 : x
  2. Step 2: Convert to fraction form
    82,410/180,858 = 180,858/x
  3. Step 3: Cross multiply
    82,410x = 180,858 × 180,858
  4. Step 4: Simplify right side
    82,410x = 32,709,616,164
  5. Step 5: Solve for x
    x = 32,709,616,164/82,410
  6. Step 6: Final answer
    x = 396,913.19

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.