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Finding the Third Proportional to 262.78 and 412.22

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Solution

The third proportional to 262.78 and 412.22 is: 646.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    262.78 : 412.22 = 412.22 : x
  2. Step 2: Convert to fraction form
    262.78/412.22 = 412.22/x
  3. Step 3: Cross multiply
    262.78x = 412.22 × 412.22
  4. Step 4: Simplify right side
    262.78x = 169,924.30
  5. Step 5: Solve for x
    x = 169,924.30/262.78
  6. Step 6: Final answer
    x = 646.64

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.