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Finding the Third Proportional to 309.75 and 470.75

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Solution

The third proportional to 309.75 and 470.75 is: 715.43

Step by Step Solution

  1. Step 1: Write the proportion equation
    309.75 : 470.75 = 470.75 : x
  2. Step 2: Convert to fraction form
    309.75/470.75 = 470.75/x
  3. Step 3: Cross multiply
    309.75x = 470.75 × 470.75
  4. Step 4: Simplify right side
    309.75x = 221,605.56
  5. Step 5: Solve for x
    x = 221,605.56/309.75
  6. Step 6: Final answer
    x = 715.43

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.