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Finding the Third Proportional to 314.25 and 470.25

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Solution

The third proportional to 314.25 and 470.25 is: 703.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    314.25 : 470.25 = 470.25 : x
  2. Step 2: Convert to fraction form
    314.25/470.25 = 470.25/x
  3. Step 3: Cross multiply
    314.25x = 470.25 × 470.25
  4. Step 4: Simplify right side
    314.25x = 221,135.06
  5. Step 5: Solve for x
    x = 221,135.06/314.25
  6. Step 6: Final answer
    x = 703.69

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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.