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Finding the Third Proportional to 209,169 and 314,231

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Solution

The third proportional to 209,169 and 314,231 is: 472,063.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    209,169 : 314,231 = 314,231 : x
  2. Step 2: Convert to fraction form
    209,169/314,231 = 314,231/x
  3. Step 3: Cross multiply
    209,169x = 314,231 × 314,231
  4. Step 4: Simplify right side
    209,169x = 98,741,121,361
  5. Step 5: Solve for x
    x = 98,741,121,361/209,169
  6. Step 6: Final answer
    x = 472,063.84

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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.