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Finding the Third Proportional to 412.88 and 455.06

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Solution

The third proportional to 412.88 and 455.06 is: 501.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    412.88 : 455.06 = 455.06 : x
  2. Step 2: Convert to fraction form
    412.88/455.06 = 455.06/x
  3. Step 3: Cross multiply
    412.88x = 455.06 × 455.06
  4. Step 4: Simplify right side
    412.88x = 207,081.88
  5. Step 5: Solve for x
    x = 207,081.88/412.88
  6. Step 6: Final answer
    x = 501.56

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.