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Finding the Third Proportional to 291 and 407

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Solution

The third proportional to 291 and 407 is: 569.24

Step by Step Solution

  1. Step 1: Write the proportion equation
    291 : 407 = 407 : x
  2. Step 2: Convert to fraction form
    291/407 = 407/x
  3. Step 3: Cross multiply
    291x = 407 × 407
  4. Step 4: Simplify right side
    291x = 165,649
  5. Step 5: Solve for x
    x = 165,649/291
  6. Step 6: Final answer
    x = 569.24

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.