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Finding the Third Proportional to 232,977 and 509,571

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Solution

The third proportional to 232,977 and 509,571 is: 1,114,541.80

Step by Step Solution

  1. Step 1: Write the proportion equation
    232,977 : 509,571 = 509,571 : x
  2. Step 2: Convert to fraction form
    232,977/509,571 = 509,571/x
  3. Step 3: Cross multiply
    232,977x = 509,571 × 509,571
  4. Step 4: Simplify right side
    232,977x = 259,662,604,041
  5. Step 5: Solve for x
    x = 259,662,604,041/232,977
  6. Step 6: Final answer
    x = 1,114,541.80

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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.