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Finding the Third Proportional to 10,596 and 13,702

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Solution

The third proportional to 10,596 and 13,702 is: 17,718.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,596 : 13,702 = 13,702 : x
  2. Step 2: Convert to fraction form
    10,596/13,702 = 13,702/x
  3. Step 3: Cross multiply
    10,596x = 13,702 × 13,702
  4. Step 4: Simplify right side
    10,596x = 187,744,804
  5. Step 5: Solve for x
    x = 187,744,804/10,596
  6. Step 6: Final answer
    x = 17,718.46

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Why These Related Problems?

These problems maintain the same ratio (1.29) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.