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Finding the Third Proportional to 13,948.50 and 19,509

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Solution

The third proportional to 13,948.50 and 19,509 is: 27,286.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,948.50 : 19,509 = 19,509 : x
  2. Step 2: Convert to fraction form
    13,948.50/19,509 = 19,509/x
  3. Step 3: Cross multiply
    13,948.50x = 19,509 × 19,509
  4. Step 4: Simplify right side
    13,948.50x = 380,601,081
  5. Step 5: Solve for x
    x = 380,601,081/13,948.50
  6. Step 6: Final answer
    x = 27,286.17

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.