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Finding the Third Proportional to 82,412 and 180,862

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Solution

The third proportional to 82,412 and 180,862 is: 396,921.12

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,412 : 180,862 = 180,862 : x
  2. Step 2: Convert to fraction form
    82,412/180,862 = 180,862/x
  3. Step 3: Cross multiply
    82,412x = 180,862 × 180,862
  4. Step 4: Simplify right side
    82,412x = 32,711,063,044
  5. Step 5: Solve for x
    x = 32,711,063,044/82,412
  6. Step 6: Final answer
    x = 396,921.12

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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.