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Finding the Third Proportional to 263,810 and 409,197

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Solution

The third proportional to 263,810 and 409,197 is: 634,707.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    263,810 : 409,197 = 409,197 : x
  2. Step 2: Convert to fraction form
    263,810/409,197 = 409,197/x
  3. Step 3: Cross multiply
    263,810x = 409,197 × 409,197
  4. Step 4: Simplify right side
    263,810x = 167,442,184,809
  5. Step 5: Solve for x
    x = 167,442,184,809/263,810
  6. Step 6: Final answer
    x = 634,707.50

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.