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Finding the Third Proportional to 13,538 and 29,506

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Solution

The third proportional to 13,538 and 29,506 is: 64,308.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,538 : 29,506 = 29,506 : x
  2. Step 2: Convert to fraction form
    13,538/29,506 = 29,506/x
  3. Step 3: Cross multiply
    13,538x = 29,506 × 29,506
  4. Step 4: Simplify right side
    13,538x = 870,604,036
  5. Step 5: Solve for x
    x = 870,604,036/13,538
  6. Step 6: Final answer
    x = 64,308.17

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.