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Finding the Third Proportional to 213.56 and 314.34

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Solution

The third proportional to 213.56 and 314.34 is: 462.68

Step by Step Solution

  1. Step 1: Write the proportion equation
    213.56 : 314.34 = 314.34 : x
  2. Step 2: Convert to fraction form
    213.56/314.34 = 314.34/x
  3. Step 3: Cross multiply
    213.56x = 314.34 × 314.34
  4. Step 4: Simplify right side
    213.56x = 98,811.99
  5. Step 5: Solve for x
    x = 98,811.99/213.56
  6. Step 6: Final answer
    x = 462.68

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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.