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Finding the Third Proportional to 7,780 and 19,282

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Solution

The third proportional to 7,780 and 19,282 is: 47,788.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,780 : 19,282 = 19,282 : x
  2. Step 2: Convert to fraction form
    7,780/19,282 = 19,282/x
  3. Step 3: Cross multiply
    7,780x = 19,282 × 19,282
  4. Step 4: Simplify right side
    7,780x = 371,795,524
  5. Step 5: Solve for x
    x = 371,795,524/7,780
  6. Step 6: Final answer
    x = 47,788.63

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Why These Related Problems?

These problems maintain the same ratio (2.48) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.