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Finding the Third Proportional to 698 and 1,083

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Solution

The third proportional to 698 and 1,083 is: 1,680.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    698 : 1,083 = 1,083 : x
  2. Step 2: Convert to fraction form
    698/1,083 = 1,083/x
  3. Step 3: Cross multiply
    698x = 1,083 × 1,083
  4. Step 4: Simplify right side
    698x = 1,172,889
  5. Step 5: Solve for x
    x = 1,172,889/698
  6. Step 6: Final answer
    x = 1,680.36

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.