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Finding the Third Proportional to 232,864 and 509,314

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Solution

The third proportional to 232,864 and 509,314 is: 1,113,958.15

Step by Step Solution

  1. Step 1: Write the proportion equation
    232,864 : 509,314 = 509,314 : x
  2. Step 2: Convert to fraction form
    232,864/509,314 = 509,314/x
  3. Step 3: Cross multiply
    232,864x = 509,314 × 509,314
  4. Step 4: Simplify right side
    232,864x = 259,400,750,596
  5. Step 5: Solve for x
    x = 259,400,750,596/232,864
  6. Step 6: Final answer
    x = 1,113,958.15

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.