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Finding the Third Proportional to 214.31 and 314.44

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Solution

The third proportional to 214.31 and 314.44 is: 461.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    214.31 : 314.44 = 314.44 : x
  2. Step 2: Convert to fraction form
    214.31/314.44 = 314.44/x
  3. Step 3: Cross multiply
    214.31x = 314.44 × 314.44
  4. Step 4: Simplify right side
    214.31x = 98,870.94
  5. Step 5: Solve for x
    x = 98,870.94/214.31
  6. Step 6: Final answer
    x = 461.34

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.