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Finding the Third Proportional to 509.63 and 1,027.69

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Solution

The third proportional to 509.63 and 1,027.69 is: 2,072.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    509.63 : 1,027.69 = 1,027.69 : x
  2. Step 2: Convert to fraction form
    509.63/1,027.69 = 1,027.69/x
  3. Step 3: Cross multiply
    509.63x = 1,027.69 × 1,027.69
  4. Step 4: Simplify right side
    509.63x = 1,056,141.60
  5. Step 5: Solve for x
    x = 1,056,141.60/509.63
  6. Step 6: Final answer
    x = 2,072.39

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Why These Related Problems?

These problems maintain the same ratio (2.02) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.