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Finding the Third Proportional to 2,597 and 3,409

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Solution

The third proportional to 2,597 and 3,409 is: 4,474.89

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,597 : 3,409 = 3,409 : x
  2. Step 2: Convert to fraction form
    2,597/3,409 = 3,409/x
  3. Step 3: Cross multiply
    2,597x = 3,409 × 3,409
  4. Step 4: Simplify right side
    2,597x = 11,621,281
  5. Step 5: Solve for x
    x = 11,621,281/2,597
  6. Step 6: Final answer
    x = 4,474.89

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Why These Related Problems?

These problems maintain the same ratio (1.31) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.