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Finding the Third Proportional to 986 and 2,597

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Solution

The third proportional to 986 and 2,597 is: 6,840.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    986 : 2,597 = 2,597 : x
  2. Step 2: Convert to fraction form
    986/2,597 = 2,597/x
  3. Step 3: Cross multiply
    986x = 2,597 × 2,597
  4. Step 4: Simplify right side
    986x = 6,744,409
  5. Step 5: Solve for x
    x = 6,744,409/986
  6. Step 6: Final answer
    x = 6,840.17

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Why These Related Problems?

These problems maintain the same ratio (2.63) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.