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Finding the Third Proportional to 416 and 781

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Solution

The third proportional to 416 and 781 is: 1,466.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    416 : 781 = 781 : x
  2. Step 2: Convert to fraction form
    416/781 = 781/x
  3. Step 3: Cross multiply
    416x = 781 × 781
  4. Step 4: Simplify right side
    416x = 609,961
  5. Step 5: Solve for x
    x = 609,961/416
  6. Step 6: Final answer
    x = 1,466.25

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Why These Related Problems?

These problems maintain the same ratio (1.88) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.