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Finding the Third Proportional to 1,265 and 1,469

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Solution

The third proportional to 1,265 and 1,469 is: 1,705.90

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,265 : 1,469 = 1,469 : x
  2. Step 2: Convert to fraction form
    1,265/1,469 = 1,469/x
  3. Step 3: Cross multiply
    1,265x = 1,469 × 1,469
  4. Step 4: Simplify right side
    1,265x = 2,157,961
  5. Step 5: Solve for x
    x = 2,157,961/1,265
  6. Step 6: Final answer
    x = 1,705.90

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Why These Related Problems?

These problems maintain the same ratio (1.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.