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Finding the Third Proportional to 12,584 and 19,486

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Solution

The third proportional to 12,584 and 19,486 is: 30,173.57

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,584 : 19,486 = 19,486 : x
  2. Step 2: Convert to fraction form
    12,584/19,486 = 19,486/x
  3. Step 3: Cross multiply
    12,584x = 19,486 × 19,486
  4. Step 4: Simplify right side
    12,584x = 379,704,196
  5. Step 5: Solve for x
    x = 379,704,196/12,584
  6. Step 6: Final answer
    x = 30,173.57

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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.