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Finding the Third Proportional to 765 and 1,678

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Solution

The third proportional to 765 and 1,678 is: 3,680.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    765 : 1,678 = 1,678 : x
  2. Step 2: Convert to fraction form
    765/1,678 = 1,678/x
  3. Step 3: Cross multiply
    765x = 1,678 × 1,678
  4. Step 4: Simplify right side
    765x = 2,815,684
  5. Step 5: Solve for x
    x = 2,815,684/765
  6. Step 6: Final answer
    x = 3,680.63

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.