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Finding the Third Proportional to 13,820 and 19,322

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Solution

The third proportional to 13,820 and 19,322 is: 27,014.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,820 : 19,322 = 19,322 : x
  2. Step 2: Convert to fraction form
    13,820/19,322 = 19,322/x
  3. Step 3: Cross multiply
    13,820x = 19,322 × 19,322
  4. Step 4: Simplify right side
    13,820x = 373,339,684
  5. Step 5: Solve for x
    x = 373,339,684/13,820
  6. Step 6: Final answer
    x = 27,014.45

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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.