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Finding the Third Proportional to 509 and 680.75

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Solution

The third proportional to 509 and 680.75 is: 910.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    509 : 680.75 = 680.75 : x
  2. Step 2: Convert to fraction form
    509/680.75 = 680.75/x
  3. Step 3: Cross multiply
    509x = 680.75 × 680.75
  4. Step 4: Simplify right side
    509x = 463,420.56
  5. Step 5: Solve for x
    x = 463,420.56/509
  6. Step 6: Final answer
    x = 910.45

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Why These Related Problems?

These problems maintain the same ratio (1.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.