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Finding the Third Proportional to 312.75 and 470.25

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Solution

The third proportional to 312.75 and 470.25 is: 707.07

Step by Step Solution

  1. Step 1: Write the proportion equation
    312.75 : 470.25 = 470.25 : x
  2. Step 2: Convert to fraction form
    312.75/470.25 = 470.25/x
  3. Step 3: Cross multiply
    312.75x = 470.25 × 470.25
  4. Step 4: Simplify right side
    312.75x = 221,135.06
  5. Step 5: Solve for x
    x = 221,135.06/312.75
  6. Step 6: Final answer
    x = 707.07

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.