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Finding the Third Proportional to 257.75 and 411.50

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Solution

The third proportional to 257.75 and 411.50 is: 656.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    257.75 : 411.50 = 411.50 : x
  2. Step 2: Convert to fraction form
    257.75/411.50 = 411.50/x
  3. Step 3: Cross multiply
    257.75x = 411.50 × 411.50
  4. Step 4: Simplify right side
    257.75x = 169,332.25
  5. Step 5: Solve for x
    x = 169,332.25/257.75
  6. Step 6: Final answer
    x = 656.96

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.