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Finding the Third Proportional to 364,414 and 509,577

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Solution

The third proportional to 364,414 and 509,577 is: 712,565.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    364,414 : 509,577 = 509,577 : x
  2. Step 2: Convert to fraction form
    364,414/509,577 = 509,577/x
  3. Step 3: Cross multiply
    364,414x = 509,577 × 509,577
  4. Step 4: Simplify right side
    364,414x = 259,668,718,929
  5. Step 5: Solve for x
    x = 259,668,718,929/364,414
  6. Step 6: Final answer
    x = 712,565.16

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.