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Finding the Third Proportional to 409.78 and 657.42

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Solution

The third proportional to 409.78 and 657.42 is: 1,054.72

Step by Step Solution

  1. Step 1: Write the proportion equation
    409.78 : 657.42 = 657.42 : x
  2. Step 2: Convert to fraction form
    409.78/657.42 = 657.42/x
  3. Step 3: Cross multiply
    409.78x = 657.42 × 657.42
  4. Step 4: Simplify right side
    409.78x = 432,203.52
  5. Step 5: Solve for x
    x = 432,203.52/409.78
  6. Step 6: Final answer
    x = 1,054.72

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.