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Finding the Third Proportional to 677 and 1,416

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Solution

The third proportional to 677 and 1,416 is: 2,961.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    677 : 1,416 = 1,416 : x
  2. Step 2: Convert to fraction form
    677/1,416 = 1,416/x
  3. Step 3: Cross multiply
    677x = 1,416 × 1,416
  4. Step 4: Simplify right side
    677x = 2,005,056
  5. Step 5: Solve for x
    x = 2,005,056/677
  6. Step 6: Final answer
    x = 2,961.68

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Why These Related Problems?

These problems maintain the same ratio (2.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.