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Finding the Third Proportional to 6,461 and 13,489

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Solution

The third proportional to 6,461 and 13,489 is: 28,161.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,461 : 13,489 = 13,489 : x
  2. Step 2: Convert to fraction form
    6,461/13,489 = 13,489/x
  3. Step 3: Cross multiply
    6,461x = 13,489 × 13,489
  4. Step 4: Simplify right side
    6,461x = 181,953,121
  5. Step 5: Solve for x
    x = 181,953,121/6,461
  6. Step 6: Final answer
    x = 28,161.76

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Why These Related Problems?

These problems maintain the same ratio (2.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.