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Finding the Third Proportional to 457 and 685

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Solution

The third proportional to 457 and 685 is: 1,026.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    457 : 685 = 685 : x
  2. Step 2: Convert to fraction form
    457/685 = 685/x
  3. Step 3: Cross multiply
    457x = 685 × 685
  4. Step 4: Simplify right side
    457x = 469,225
  5. Step 5: Solve for x
    x = 469,225/457
  6. Step 6: Final answer
    x = 1,026.75

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.