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Finding the Third Proportional to 854 and 1,306

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Solution

The third proportional to 854 and 1,306 is: 1,997.23

Step by Step Solution

  1. Step 1: Write the proportion equation
    854 : 1,306 = 1,306 : x
  2. Step 2: Convert to fraction form
    854/1,306 = 1,306/x
  3. Step 3: Cross multiply
    854x = 1,306 × 1,306
  4. Step 4: Simplify right side
    854x = 1,705,636
  5. Step 5: Solve for x
    x = 1,705,636/854
  6. Step 6: Final answer
    x = 1,997.23

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.