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Finding the Third Proportional to 7,772 and 16,324

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Solution

The third proportional to 7,772 and 16,324 is: 34,286.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,772 : 16,324 = 16,324 : x
  2. Step 2: Convert to fraction form
    7,772/16,324 = 16,324/x
  3. Step 3: Cross multiply
    7,772x = 16,324 × 16,324
  4. Step 4: Simplify right side
    7,772x = 266,472,976
  5. Step 5: Solve for x
    x = 266,472,976/7,772
  6. Step 6: Final answer
    x = 34,286.28

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Why These Related Problems?

These problems maintain the same ratio (2.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.