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Finding the Third Proportional to 214.75 and 412.25

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Solution

The third proportional to 214.75 and 412.25 is: 791.39

Step by Step Solution

  1. Step 1: Write the proportion equation
    214.75 : 412.25 = 412.25 : x
  2. Step 2: Convert to fraction form
    214.75/412.25 = 412.25/x
  3. Step 3: Cross multiply
    214.75x = 412.25 × 412.25
  4. Step 4: Simplify right side
    214.75x = 169,950.06
  5. Step 5: Solve for x
    x = 169,950.06/214.75
  6. Step 6: Final answer
    x = 791.39

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Why These Related Problems?

These problems maintain the same ratio (1.92) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.