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Finding the Third Proportional to 509.63 and 643.78

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Solution

The third proportional to 509.63 and 643.78 is: 813.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    509.63 : 643.78 = 643.78 : x
  2. Step 2: Convert to fraction form
    509.63/643.78 = 643.78/x
  3. Step 3: Cross multiply
    509.63x = 643.78 × 643.78
  4. Step 4: Simplify right side
    509.63x = 414,454.30
  5. Step 5: Solve for x
    x = 414,454.30/509.63
  6. Step 6: Final answer
    x = 813.25

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Why These Related Problems?

These problems maintain the same ratio (1.26) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.