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Finding the Third Proportional to 509 and 1,289

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Solution

The third proportional to 509 and 1,289 is: 3,264.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    509 : 1,289 = 1,289 : x
  2. Step 2: Convert to fraction form
    509/1,289 = 1,289/x
  3. Step 3: Cross multiply
    509x = 1,289 × 1,289
  4. Step 4: Simplify right side
    509x = 1,661,521
  5. Step 5: Solve for x
    x = 1,661,521/509
  6. Step 6: Final answer
    x = 3,264.28

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Why These Related Problems?

These problems maintain the same ratio (2.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.