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Finding the Third Proportional to 4,223 and 9,684

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Solution

The third proportional to 4,223 and 9,684 is: 22,206.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,223 : 9,684 = 9,684 : x
  2. Step 2: Convert to fraction form
    4,223/9,684 = 9,684/x
  3. Step 3: Cross multiply
    4,223x = 9,684 × 9,684
  4. Step 4: Simplify right side
    4,223x = 93,779,856
  5. Step 5: Solve for x
    x = 93,779,856/4,223
  6. Step 6: Final answer
    x = 22,206.93

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Why These Related Problems?

These problems maintain the same ratio (2.29) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.