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Finding the Third Proportional to 232,986 and 509,590

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Solution

The third proportional to 232,986 and 509,590 is: 1,114,581.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    232,986 : 509,590 = 509,590 : x
  2. Step 2: Convert to fraction form
    232,986/509,590 = 509,590/x
  3. Step 3: Cross multiply
    232,986x = 509,590 × 509,590
  4. Step 4: Simplify right side
    232,986x = 259,681,968,100
  5. Step 5: Solve for x
    x = 259,681,968,100/232,986
  6. Step 6: Final answer
    x = 1,114,581.86

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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.