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Finding the Third Proportional to 1,297 and 2,058

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Solution

The third proportional to 1,297 and 2,058 is: 3,265.51

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,297 : 2,058 = 2,058 : x
  2. Step 2: Convert to fraction form
    1,297/2,058 = 2,058/x
  3. Step 3: Cross multiply
    1,297x = 2,058 × 2,058
  4. Step 4: Simplify right side
    1,297x = 4,235,364
  5. Step 5: Solve for x
    x = 4,235,364/1,297
  6. Step 6: Final answer
    x = 3,265.51

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.