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Finding the Third Proportional to 2,597 and 5,407

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Solution

The third proportional to 2,597 and 5,407 is: 11,257.47

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,597 : 5,407 = 5,407 : x
  2. Step 2: Convert to fraction form
    2,597/5,407 = 5,407/x
  3. Step 3: Cross multiply
    2,597x = 5,407 × 5,407
  4. Step 4: Simplify right side
    2,597x = 29,235,649
  5. Step 5: Solve for x
    x = 29,235,649/2,597
  6. Step 6: Final answer
    x = 11,257.47

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.