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Finding the Third Proportional to 9,735 and 13,407

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Solution

The third proportional to 9,735 and 13,407 is: 18,464.06

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,735 : 13,407 = 13,407 : x
  2. Step 2: Convert to fraction form
    9,735/13,407 = 13,407/x
  3. Step 3: Cross multiply
    9,735x = 13,407 × 13,407
  4. Step 4: Simplify right side
    9,735x = 179,747,649
  5. Step 5: Solve for x
    x = 179,747,649/9,735
  6. Step 6: Final answer
    x = 18,464.06

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.