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Finding the Third Proportional to 97.50 and 214.13

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Solution

The third proportional to 97.50 and 214.13 is: 470.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    97.50 : 214.13 = 214.13 : x
  2. Step 2: Convert to fraction form
    97.50/214.13 = 214.13/x
  3. Step 3: Cross multiply
    97.50x = 214.13 × 214.13
  4. Step 4: Simplify right side
    97.50x = 45,849.52
  5. Step 5: Solve for x
    x = 45,849.52/97.50
  6. Step 6: Final answer
    x = 470.25

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.