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Finding the Third Proportional to 412.75 and 857.50

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Solution

The third proportional to 412.75 and 857.50 is: 1,781.48

Step by Step Solution

  1. Step 1: Write the proportion equation
    412.75 : 857.50 = 857.50 : x
  2. Step 2: Convert to fraction form
    412.75/857.50 = 857.50/x
  3. Step 3: Cross multiply
    412.75x = 857.50 × 857.50
  4. Step 4: Simplify right side
    412.75x = 735,306.25
  5. Step 5: Solve for x
    x = 735,306.25/412.75
  6. Step 6: Final answer
    x = 1,781.48

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.