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Finding the Third Proportional to 2,597 and 5,239

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Solution

The third proportional to 2,597 and 5,239 is: 10,568.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,597 : 5,239 = 5,239 : x
  2. Step 2: Convert to fraction form
    2,597/5,239 = 5,239/x
  3. Step 3: Cross multiply
    2,597x = 5,239 × 5,239
  4. Step 4: Simplify right side
    2,597x = 27,447,121
  5. Step 5: Solve for x
    x = 27,447,121/2,597
  6. Step 6: Final answer
    x = 10,568.78

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Why These Related Problems?

These problems maintain the same ratio (2.02) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.