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Finding the Third Proportional to 398.50 and 431.50

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Solution

The third proportional to 398.50 and 431.50 is: 467.23

Step by Step Solution

  1. Step 1: Write the proportion equation
    398.50 : 431.50 = 431.50 : x
  2. Step 2: Convert to fraction form
    398.50/431.50 = 431.50/x
  3. Step 3: Cross multiply
    398.50x = 431.50 × 431.50
  4. Step 4: Simplify right side
    398.50x = 186,192.25
  5. Step 5: Solve for x
    x = 186,192.25/398.50
  6. Step 6: Final answer
    x = 467.23

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.