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Finding the Third Proportional to 82,454 and 180,689

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Solution

The third proportional to 82,454 and 180,689 is: 395,960.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,454 : 180,689 = 180,689 : x
  2. Step 2: Convert to fraction form
    82,454/180,689 = 180,689/x
  3. Step 3: Cross multiply
    82,454x = 180,689 × 180,689
  4. Step 4: Simplify right side
    82,454x = 32,648,514,721
  5. Step 5: Solve for x
    x = 32,648,514,721/82,454
  6. Step 6: Final answer
    x = 395,960.35

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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.