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Finding the Third Proportional to 9,710 and 20,464

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Solution

The third proportional to 9,710 and 20,464 is: 43,128.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,710 : 20,464 = 20,464 : x
  2. Step 2: Convert to fraction form
    9,710/20,464 = 20,464/x
  3. Step 3: Cross multiply
    9,710x = 20,464 × 20,464
  4. Step 4: Simplify right side
    9,710x = 418,775,296
  5. Step 5: Solve for x
    x = 418,775,296/9,710
  6. Step 6: Final answer
    x = 43,128.25

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Why These Related Problems?

These problems maintain the same ratio (2.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.