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Finding the Third Proportional to 309.75 and 418.13

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Solution

The third proportional to 309.75 and 418.13 is: 564.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    309.75 : 418.13 = 418.13 : x
  2. Step 2: Convert to fraction form
    309.75/418.13 = 418.13/x
  3. Step 3: Cross multiply
    309.75x = 418.13 × 418.13
  4. Step 4: Simplify right side
    309.75x = 174,828.52
  5. Step 5: Solve for x
    x = 174,828.52/309.75
  6. Step 6: Final answer
    x = 564.42

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Why These Related Problems?

These problems maintain the same ratio (1.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.