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Finding the Third Proportional to 19,746 and 31,403

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Solution

The third proportional to 19,746 and 31,403 is: 49,941.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    19,746 : 31,403 = 31,403 : x
  2. Step 2: Convert to fraction form
    19,746/31,403 = 31,403/x
  3. Step 3: Cross multiply
    19,746x = 31,403 × 31,403
  4. Step 4: Simplify right side
    19,746x = 986,148,409
  5. Step 5: Solve for x
    x = 986,148,409/19,746
  6. Step 6: Final answer
    x = 49,941.68

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.