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Finding the Third Proportional to 12,296 and 19,776

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Solution

The third proportional to 12,296 and 19,776 is: 31,806.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,296 : 19,776 = 19,776 : x
  2. Step 2: Convert to fraction form
    12,296/19,776 = 19,776/x
  3. Step 3: Cross multiply
    12,296x = 19,776 × 19,776
  4. Step 4: Simplify right side
    12,296x = 391,090,176
  5. Step 5: Solve for x
    x = 391,090,176/12,296
  6. Step 6: Final answer
    x = 31,806.29

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.