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Finding the Third Proportional to 509 and 1,265

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Solution

The third proportional to 509 and 1,265 is: 3,143.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    509 : 1,265 = 1,265 : x
  2. Step 2: Convert to fraction form
    509/1,265 = 1,265/x
  3. Step 3: Cross multiply
    509x = 1,265 × 1,265
  4. Step 4: Simplify right side
    509x = 1,600,225
  5. Step 5: Solve for x
    x = 1,600,225/509
  6. Step 6: Final answer
    x = 3,143.86

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Why These Related Problems?

These problems maintain the same ratio (2.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.