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Finding the Third Proportional to 19,680 and 31,296

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Solution

The third proportional to 19,680 and 31,296 is: 49,768.27

Step by Step Solution

  1. Step 1: Write the proportion equation
    19,680 : 31,296 = 31,296 : x
  2. Step 2: Convert to fraction form
    19,680/31,296 = 31,296/x
  3. Step 3: Cross multiply
    19,680x = 31,296 × 31,296
  4. Step 4: Simplify right side
    19,680x = 979,439,616
  5. Step 5: Solve for x
    x = 979,439,616/19,680
  6. Step 6: Final answer
    x = 49,768.27

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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.