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Finding the Third Proportional to 5,306 and 11,456

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Solution

The third proportional to 5,306 and 11,456 is: 24,734.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,306 : 11,456 = 11,456 : x
  2. Step 2: Convert to fraction form
    5,306/11,456 = 11,456/x
  3. Step 3: Cross multiply
    5,306x = 11,456 × 11,456
  4. Step 4: Simplify right side
    5,306x = 131,239,936
  5. Step 5: Solve for x
    x = 131,239,936/5,306
  6. Step 6: Final answer
    x = 24,734.25

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.