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Finding the Third Proportional to 768 and 1,680

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Solution

The third proportional to 768 and 1,680 is: 3,675

Step by Step Solution

  1. Step 1: Write the proportion equation
    768 : 1,680 = 1,680 : x
  2. Step 2: Convert to fraction form
    768/1,680 = 1,680/x
  3. Step 3: Cross multiply
    768x = 1,680 × 1,680
  4. Step 4: Simplify right side
    768x = 2,822,400
  5. Step 5: Solve for x
    x = 2,822,400/768
  6. Step 6: Final answer
    x = 3,675

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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.