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Finding the Third Proportional to 232,976 and 509,570

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Solution

The third proportional to 232,976 and 509,570 is: 1,114,542.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    232,976 : 509,570 = 509,570 : x
  2. Step 2: Convert to fraction form
    232,976/509,570 = 509,570/x
  3. Step 3: Cross multiply
    232,976x = 509,570 × 509,570
  4. Step 4: Simplify right side
    232,976x = 259,661,584,900
  5. Step 5: Solve for x
    x = 259,661,584,900/232,976
  6. Step 6: Final answer
    x = 1,114,542.21

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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.