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Finding the Third Proportional to 407 and 491

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Solution

The third proportional to 407 and 491 is: 592.34

Step by Step Solution

  1. Step 1: Write the proportion equation
    407 : 491 = 491 : x
  2. Step 2: Convert to fraction form
    407/491 = 491/x
  3. Step 3: Cross multiply
    407x = 491 × 491
  4. Step 4: Simplify right side
    407x = 241,081
  5. Step 5: Solve for x
    x = 241,081/407
  6. Step 6: Final answer
    x = 592.34

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Why These Related Problems?

These problems maintain the same ratio (1.21) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.