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Finding the Third Proportional to 412 and 986.50

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Solution

The third proportional to 412 and 986.50 is: 2,362.09

Step by Step Solution

  1. Step 1: Write the proportion equation
    412 : 986.50 = 986.50 : x
  2. Step 2: Convert to fraction form
    412/986.50 = 986.50/x
  3. Step 3: Cross multiply
    412x = 986.50 × 986.50
  4. Step 4: Simplify right side
    412x = 973,182.25
  5. Step 5: Solve for x
    x = 973,182.25/412
  6. Step 6: Final answer
    x = 2,362.09

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Why These Related Problems?

These problems maintain the same ratio (2.39) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.