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Finding the Third Proportional to 232,852 and 509,296

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Solution

The third proportional to 232,852 and 509,296 is: 1,113,936.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    232,852 : 509,296 = 509,296 : x
  2. Step 2: Convert to fraction form
    232,852/509,296 = 509,296/x
  3. Step 3: Cross multiply
    232,852x = 509,296 × 509,296
  4. Step 4: Simplify right side
    232,852x = 259,382,415,616
  5. Step 5: Solve for x
    x = 259,382,415,616/232,852
  6. Step 6: Final answer
    x = 1,113,936.82

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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.