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Finding the Third Proportional to 782 and 1,029

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Solution

The third proportional to 782 and 1,029 is: 1,354.02

Step by Step Solution

  1. Step 1: Write the proportion equation
    782 : 1,029 = 1,029 : x
  2. Step 2: Convert to fraction form
    782/1,029 = 1,029/x
  3. Step 3: Cross multiply
    782x = 1,029 × 1,029
  4. Step 4: Simplify right side
    782x = 1,058,841
  5. Step 5: Solve for x
    x = 1,058,841/782
  6. Step 6: Final answer
    x = 1,354.02

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Why These Related Problems?

These problems maintain the same ratio (1.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.