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Finding the Third Proportional to 7,730 and 11,597

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Solution

The third proportional to 7,730 and 11,597 is: 17,398.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,730 : 11,597 = 11,597 : x
  2. Step 2: Convert to fraction form
    7,730/11,597 = 11,597/x
  3. Step 3: Cross multiply
    7,730x = 11,597 × 11,597
  4. Step 4: Simplify right side
    7,730x = 134,490,409
  5. Step 5: Solve for x
    x = 134,490,409/7,730
  6. Step 6: Final answer
    x = 17,398.50

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.