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Finding the Third Proportional to 230.25 and 309.75

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Solution

The third proportional to 230.25 and 309.75 is: 416.70

Step by Step Solution

  1. Step 1: Write the proportion equation
    230.25 : 309.75 = 309.75 : x
  2. Step 2: Convert to fraction form
    230.25/309.75 = 309.75/x
  3. Step 3: Cross multiply
    230.25x = 309.75 × 309.75
  4. Step 4: Simplify right side
    230.25x = 95,945.06
  5. Step 5: Solve for x
    x = 95,945.06/230.25
  6. Step 6: Final answer
    x = 416.70

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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.