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Finding the Third Proportional to 82,457 and 180,695

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Solution

The third proportional to 82,457 and 180,695 is: 395,972.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    82,457 : 180,695 = 180,695 : x
  2. Step 2: Convert to fraction form
    82,457/180,695 = 180,695/x
  3. Step 3: Cross multiply
    82,457x = 180,695 × 180,695
  4. Step 4: Simplify right side
    82,457x = 32,650,683,025
  5. Step 5: Solve for x
    x = 32,650,683,025/82,457
  6. Step 6: Final answer
    x = 395,972.24

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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.