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Finding the Third Proportional to 209.78 and 458.47

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Solution

The third proportional to 209.78 and 458.47 is: 1,002.00

Step by Step Solution

  1. Step 1: Write the proportion equation
    209.78 : 458.47 = 458.47 : x
  2. Step 2: Convert to fraction form
    209.78/458.47 = 458.47/x
  3. Step 3: Cross multiply
    209.78x = 458.47 × 458.47
  4. Step 4: Simplify right side
    209.78x = 210,197.18
  5. Step 5: Solve for x
    x = 210,197.18/209.78
  6. Step 6: Final answer
    x = 1,002.00

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.