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Finding the Third Proportional to 13,198 and 19,784

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Solution

The third proportional to 13,198 and 19,784 is: 29,656.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,198 : 19,784 = 19,784 : x
  2. Step 2: Convert to fraction form
    13,198/19,784 = 19,784/x
  3. Step 3: Cross multiply
    13,198x = 19,784 × 19,784
  4. Step 4: Simplify right side
    13,198x = 391,406,656
  5. Step 5: Solve for x
    x = 391,406,656/13,198
  6. Step 6: Final answer
    x = 29,656.51

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.