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Finding the Third Proportional to 19,664 and 31,430

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Solution

The third proportional to 19,664 and 31,430 is: 50,236.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    19,664 : 31,430 = 31,430 : x
  2. Step 2: Convert to fraction form
    19,664/31,430 = 31,430/x
  3. Step 3: Cross multiply
    19,664x = 31,430 × 31,430
  4. Step 4: Simplify right side
    19,664x = 987,844,900
  5. Step 5: Solve for x
    x = 987,844,900/19,664
  6. Step 6: Final answer
    x = 50,236.21

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.