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Finding the Third Proportional to 208.50 and 422.63

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Solution

The third proportional to 208.50 and 422.63 is: 856.65

Step by Step Solution

  1. Step 1: Write the proportion equation
    208.50 : 422.63 = 422.63 : x
  2. Step 2: Convert to fraction form
    208.50/422.63 = 422.63/x
  3. Step 3: Cross multiply
    208.50x = 422.63 × 422.63
  4. Step 4: Simplify right side
    208.50x = 178,611.89
  5. Step 5: Solve for x
    x = 178,611.89/208.50
  6. Step 6: Final answer
    x = 856.65

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Why These Related Problems?

These problems maintain the same ratio (2.03) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.