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Finding the Third Proportional to 27,407 and 42,814

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Solution

The third proportional to 27,407 and 42,814 is: 66,882.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    27,407 : 42,814 = 42,814 : x
  2. Step 2: Convert to fraction form
    27,407/42,814 = 42,814/x
  3. Step 3: Cross multiply
    27,407x = 42,814 × 42,814
  4. Step 4: Simplify right side
    27,407x = 1,833,038,596
  5. Step 5: Solve for x
    x = 1,833,038,596/27,407
  6. Step 6: Final answer
    x = 66,882.13

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Why These Related Problems?

These problems maintain the same ratio (1.56) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.