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Finding the Third Proportional to 782 and 1,444

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Solution

The third proportional to 782 and 1,444 is: 2,666.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    782 : 1,444 = 1,444 : x
  2. Step 2: Convert to fraction form
    782/1,444 = 1,444/x
  3. Step 3: Cross multiply
    782x = 1,444 × 1,444
  4. Step 4: Simplify right side
    782x = 2,085,136
  5. Step 5: Solve for x
    x = 2,085,136/782
  6. Step 6: Final answer
    x = 2,666.41

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Why These Related Problems?

These problems maintain the same ratio (1.85) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.