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Finding the Third Proportional to 257.50 and 698.50

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Solution

The third proportional to 257.50 and 698.50 is: 1,894.77

Step by Step Solution

  1. Step 1: Write the proportion equation
    257.50 : 698.50 = 698.50 : x
  2. Step 2: Convert to fraction form
    257.50/698.50 = 698.50/x
  3. Step 3: Cross multiply
    257.50x = 698.50 × 698.50
  4. Step 4: Simplify right side
    257.50x = 487,902.25
  5. Step 5: Solve for x
    x = 487,902.25/257.50
  6. Step 6: Final answer
    x = 1,894.77

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Why These Related Problems?

These problems maintain the same ratio (2.71) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.