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Finding the Third Proportional to 1,783 and 2,098

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Solution

The third proportional to 1,783 and 2,098 is: 2,468.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,783 : 2,098 = 2,098 : x
  2. Step 2: Convert to fraction form
    1,783/2,098 = 2,098/x
  3. Step 3: Cross multiply
    1,783x = 2,098 × 2,098
  4. Step 4: Simplify right side
    1,783x = 4,401,604
  5. Step 5: Solve for x
    x = 4,401,604/1,783
  6. Step 6: Final answer
    x = 2,468.65

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Why These Related Problems?

These problems maintain the same ratio (1.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.