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Finding the Third Proportional to 9,724 and 23,306

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Solution

The third proportional to 9,724 and 23,306 is: 55,858.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    9,724 : 23,306 = 23,306 : x
  2. Step 2: Convert to fraction form
    9,724/23,306 = 23,306/x
  3. Step 3: Cross multiply
    9,724x = 23,306 × 23,306
  4. Step 4: Simplify right side
    9,724x = 543,169,636
  5. Step 5: Solve for x
    x = 543,169,636/9,724
  6. Step 6: Final answer
    x = 55,858.66

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Why These Related Problems?

These problems maintain the same ratio (2.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.