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Finding the Third Proportional to 209,741 and 314,634

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Solution

The third proportional to 209,741 and 314,634 is: 471,984.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    209,741 : 314,634 = 314,634 : x
  2. Step 2: Convert to fraction form
    209,741/314,634 = 314,634/x
  3. Step 3: Cross multiply
    209,741x = 314,634 × 314,634
  4. Step 4: Simplify right side
    209,741x = 98,994,553,956
  5. Step 5: Solve for x
    x = 98,994,553,956/209,741
  6. Step 6: Final answer
    x = 471,984.75

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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.