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Finding the Third Proportional to 19,712 and 31,209

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Solution

The third proportional to 19,712 and 31,209 is: 49,411.61

Step by Step Solution

  1. Step 1: Write the proportion equation
    19,712 : 31,209 = 31,209 : x
  2. Step 2: Convert to fraction form
    19,712/31,209 = 31,209/x
  3. Step 3: Cross multiply
    19,712x = 31,209 × 31,209
  4. Step 4: Simplify right side
    19,712x = 974,001,681
  5. Step 5: Solve for x
    x = 974,001,681/19,712
  6. Step 6: Final answer
    x = 49,411.61

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Why These Related Problems?

These problems maintain the same ratio (1.58) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.