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Finding the Third Proportional to 409 and 761

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Solution

The third proportional to 409 and 761 is: 1,415.94

Step by Step Solution

  1. Step 1: Write the proportion equation
    409 : 761 = 761 : x
  2. Step 2: Convert to fraction form
    409/761 = 761/x
  3. Step 3: Cross multiply
    409x = 761 × 761
  4. Step 4: Simplify right side
    409x = 579,121
  5. Step 5: Solve for x
    x = 579,121/409
  6. Step 6: Final answer
    x = 1,415.94

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Why These Related Problems?

These problems maintain the same ratio (1.86) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.