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Finding the Third Proportional to 6,510 and 9,735

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Solution

The third proportional to 6,510 and 9,735 is: 14,557.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,510 : 9,735 = 9,735 : x
  2. Step 2: Convert to fraction form
    6,510/9,735 = 9,735/x
  3. Step 3: Cross multiply
    6,510x = 9,735 × 9,735
  4. Step 4: Simplify right side
    6,510x = 94,770,225
  5. Step 5: Solve for x
    x = 94,770,225/6,510
  6. Step 6: Final answer
    x = 14,557.64

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.