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Finding the Third Proportional to 27,942 and 40,409

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Solution

The third proportional to 27,942 and 40,409 is: 58,438.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    27,942 : 40,409 = 40,409 : x
  2. Step 2: Convert to fraction form
    27,942/40,409 = 40,409/x
  3. Step 3: Cross multiply
    27,942x = 40,409 × 40,409
  4. Step 4: Simplify right side
    27,942x = 1,632,887,281
  5. Step 5: Solve for x
    x = 1,632,887,281/27,942
  6. Step 6: Final answer
    x = 58,438.45

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Why These Related Problems?

These problems maintain the same ratio (1.45) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.