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Finding the Third Proportional to 7,470 and 9,729

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Solution

The third proportional to 7,470 and 9,729 is: 12,671.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,470 : 9,729 = 9,729 : x
  2. Step 2: Convert to fraction form
    7,470/9,729 = 9,729/x
  3. Step 3: Cross multiply
    7,470x = 9,729 × 9,729
  4. Step 4: Simplify right side
    7,470x = 94,653,441
  5. Step 5: Solve for x
    x = 94,653,441/7,470
  6. Step 6: Final answer
    x = 12,671.14

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Why These Related Problems?

These problems maintain the same ratio (1.30) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.