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Finding the Third Proportional to 2,164 and 4,616

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Solution

The third proportional to 2,164 and 4,616 is: 9,846.33

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,164 : 4,616 = 4,616 : x
  2. Step 2: Convert to fraction form
    2,164/4,616 = 4,616/x
  3. Step 3: Cross multiply
    2,164x = 4,616 × 4,616
  4. Step 4: Simplify right side
    2,164x = 21,307,456
  5. Step 5: Solve for x
    x = 21,307,456/2,164
  6. Step 6: Final answer
    x = 9,846.33

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.