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Finding the Third Proportional to 19,506 and 31,411

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Solution

The third proportional to 19,506 and 31,411 is: 50,581.92

Step by Step Solution

  1. Step 1: Write the proportion equation
    19,506 : 31,411 = 31,411 : x
  2. Step 2: Convert to fraction form
    19,506/31,411 = 31,411/x
  3. Step 3: Cross multiply
    19,506x = 31,411 × 31,411
  4. Step 4: Simplify right side
    19,506x = 986,650,921
  5. Step 5: Solve for x
    x = 986,650,921/19,506
  6. Step 6: Final answer
    x = 50,581.92

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.