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Finding the Third Proportional to 412 and 686.50

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Solution

The third proportional to 412 and 686.50 is: 1,143.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    412 : 686.50 = 686.50 : x
  2. Step 2: Convert to fraction form
    412/686.50 = 686.50/x
  3. Step 3: Cross multiply
    412x = 686.50 × 686.50
  4. Step 4: Simplify right side
    412x = 471,282.25
  5. Step 5: Solve for x
    x = 471,282.25/412
  6. Step 6: Final answer
    x = 1,143.89

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Why These Related Problems?

These problems maintain the same ratio (1.67) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.