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Finding the Third Proportional to 6,590 and 9,257

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Solution

The third proportional to 6,590 and 9,257 is: 13,003.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,590 : 9,257 = 9,257 : x
  2. Step 2: Convert to fraction form
    6,590/9,257 = 9,257/x
  3. Step 3: Cross multiply
    6,590x = 9,257 × 9,257
  4. Step 4: Simplify right side
    6,590x = 85,692,049
  5. Step 5: Solve for x
    x = 85,692,049/6,590
  6. Step 6: Final answer
    x = 13,003.35

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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.