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Finding the Third Proportional to 9,646 and 22,409

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Solution

The third proportional to 9,646 and 22,409 is: 52,059.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,646 : 22,409 = 22,409 : x
  2. Step 2: Convert to fraction form
    9,646/22,409 = 22,409/x
  3. Step 3: Cross multiply
    9,646x = 22,409 × 22,409
  4. Step 4: Simplify right side
    9,646x = 502,163,281
  5. Step 5: Solve for x
    x = 502,163,281/9,646
  6. Step 6: Final answer
    x = 52,059.22

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Why These Related Problems?

These problems maintain the same ratio (2.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.