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Finding the Third Proportional to 37,814 and 81,409

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Solution

The third proportional to 37,814 and 81,409 is: 175,263.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    37,814 : 81,409 = 81,409 : x
  2. Step 2: Convert to fraction form
    37,814/81,409 = 81,409/x
  3. Step 3: Cross multiply
    37,814x = 81,409 × 81,409
  4. Step 4: Simplify right side
    37,814x = 6,627,425,281
  5. Step 5: Solve for x
    x = 6,627,425,281/37,814
  6. Step 6: Final answer
    x = 175,263.80

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Why These Related Problems?

These problems maintain the same ratio (2.15) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.