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Finding the Third Proportional to 12,284 and 19,057

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Solution

The third proportional to 12,284 and 19,057 is: 29,564.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,284 : 19,057 = 19,057 : x
  2. Step 2: Convert to fraction form
    12,284/19,057 = 19,057/x
  3. Step 3: Cross multiply
    12,284x = 19,057 × 19,057
  4. Step 4: Simplify right side
    12,284x = 363,169,249
  5. Step 5: Solve for x
    x = 363,169,249/12,284
  6. Step 6: Final answer
    x = 29,564.41

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.