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Finding the Third Proportional to 83,782 and 180,682

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Solution

The third proportional to 83,782 and 180,682 is: 389,653.92

Step by Step Solution

  1. Step 1: Write the proportion equation
    83,782 : 180,682 = 180,682 : x
  2. Step 2: Convert to fraction form
    83,782/180,682 = 180,682/x
  3. Step 3: Cross multiply
    83,782x = 180,682 × 180,682
  4. Step 4: Simplify right side
    83,782x = 32,645,985,124
  5. Step 5: Solve for x
    x = 32,645,985,124/83,782
  6. Step 6: Final answer
    x = 389,653.92

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.