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Finding the Third Proportional to 783 and 1,690

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Solution

The third proportional to 783 and 1,690 is: 3,647.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    783 : 1,690 = 1,690 : x
  2. Step 2: Convert to fraction form
    783/1,690 = 1,690/x
  3. Step 3: Cross multiply
    783x = 1,690 × 1,690
  4. Step 4: Simplify right side
    783x = 2,856,100
  5. Step 5: Solve for x
    x = 2,856,100/783
  6. Step 6: Final answer
    x = 3,647.64

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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.