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Finding the Third Proportional to 205,109 and 310,493.50

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Solution

The third proportional to 205,109 and 310,493.50 is: 470,024.30

Step by Step Solution

  1. Step 1: Write the proportion equation
    205,109 : 310,493.50 = 310,493.50 : x
  2. Step 2: Convert to fraction form
    205,109/310,493.50 = 310,493.50/x
  3. Step 3: Cross multiply
    205,109x = 310,493.50 × 310,493.50
  4. Step 4: Simplify right side
    205,109x = 96,406,213,542.25
  5. Step 5: Solve for x
    x = 96,406,213,542.25/205,109
  6. Step 6: Final answer
    x = 470,024.30

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.