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Finding the Third Proportional to 9,709 and 20,964

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Solution

The third proportional to 9,709 and 20,964 is: 45,266.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,709 : 20,964 = 20,964 : x
  2. Step 2: Convert to fraction form
    9,709/20,964 = 20,964/x
  3. Step 3: Cross multiply
    9,709x = 20,964 × 20,964
  4. Step 4: Simplify right side
    9,709x = 439,489,296
  5. Step 5: Solve for x
    x = 439,489,296/9,709
  6. Step 6: Final answer
    x = 45,266.18

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.