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Finding the Third Proportional to 135,416 and 206,144

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Solution

The third proportional to 135,416 and 206,144 is: 313,813.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    135,416 : 206,144 = 206,144 : x
  2. Step 2: Convert to fraction form
    135,416/206,144 = 206,144/x
  3. Step 3: Cross multiply
    135,416x = 206,144 × 206,144
  4. Step 4: Simplify right side
    135,416x = 42,495,348,736
  5. Step 5: Solve for x
    x = 42,495,348,736/135,416
  6. Step 6: Final answer
    x = 313,813.35

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Why These Related Problems?

These problems maintain the same ratio (1.52) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.