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Finding the Third Proportional to 12,378 and 19,680

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Solution

The third proportional to 12,378 and 19,680 is: 31,289.58

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,378 : 19,680 = 19,680 : x
  2. Step 2: Convert to fraction form
    12,378/19,680 = 19,680/x
  3. Step 3: Cross multiply
    12,378x = 19,680 × 19,680
  4. Step 4: Simplify right side
    12,378x = 387,302,400
  5. Step 5: Solve for x
    x = 387,302,400/12,378
  6. Step 6: Final answer
    x = 31,289.58

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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.