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Finding the Third Proportional to 412.78 and 986.53

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Solution

The third proportional to 412.78 and 986.53 is: 2,357.77

Step by Step Solution

  1. Step 1: Write the proportion equation
    412.78 : 986.53 = 986.53 : x
  2. Step 2: Convert to fraction form
    412.78/986.53 = 986.53/x
  3. Step 3: Cross multiply
    412.78x = 986.53 × 986.53
  4. Step 4: Simplify right side
    412.78x = 973,243.91
  5. Step 5: Solve for x
    x = 973,243.91/412.78
  6. Step 6: Final answer
    x = 2,357.77

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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.