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Finding the Third Proportional to 106.50 and 257.50

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Solution

The third proportional to 106.50 and 257.50 is: 622.59

Step by Step Solution

  1. Step 1: Write the proportion equation
    106.50 : 257.50 = 257.50 : x
  2. Step 2: Convert to fraction form
    106.50/257.50 = 257.50/x
  3. Step 3: Cross multiply
    106.50x = 257.50 × 257.50
  4. Step 4: Simplify right side
    106.50x = 66,306.25
  5. Step 5: Solve for x
    x = 66,306.25/106.50
  6. Step 6: Final answer
    x = 622.59

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Why These Related Problems?

These problems maintain the same ratio (2.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.