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Finding the Third Proportional to 257.63 and 421.88

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Solution

The third proportional to 257.63 and 421.88 is: 690.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    257.63 : 421.88 = 421.88 : x
  2. Step 2: Convert to fraction form
    257.63/421.88 = 421.88/x
  3. Step 3: Cross multiply
    257.63x = 421.88 × 421.88
  4. Step 4: Simplify right side
    257.63x = 177,978.52
  5. Step 5: Solve for x
    x = 177,978.52/257.63
  6. Step 6: Final answer
    x = 690.84

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Why These Related Problems?

These problems maintain the same ratio (1.64) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.