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Finding the Third Proportional to 712 and 1,691

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Solution

The third proportional to 712 and 1,691 is: 4,016.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    712 : 1,691 = 1,691 : x
  2. Step 2: Convert to fraction form
    712/1,691 = 1,691/x
  3. Step 3: Cross multiply
    712x = 1,691 × 1,691
  4. Step 4: Simplify right side
    712x = 2,859,481
  5. Step 5: Solve for x
    x = 2,859,481/712
  6. Step 6: Final answer
    x = 4,016.13

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Why These Related Problems?

These problems maintain the same ratio (2.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.