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Finding the Third Proportional to 209,166 and 314,226

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Solution

The third proportional to 209,166 and 314,226 is: 472,055.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    209,166 : 314,226 = 314,226 : x
  2. Step 2: Convert to fraction form
    209,166/314,226 = 314,226/x
  3. Step 3: Cross multiply
    209,166x = 314,226 × 314,226
  4. Step 4: Simplify right side
    209,166x = 98,737,979,076
  5. Step 5: Solve for x
    x = 98,737,979,076/209,166
  6. Step 6: Final answer
    x = 472,055.59

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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.