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Finding the Third Proportional to 7,702 and 12,403

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Solution

The third proportional to 7,702 and 12,403 is: 19,973.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,702 : 12,403 = 12,403 : x
  2. Step 2: Convert to fraction form
    7,702/12,403 = 12,403/x
  3. Step 3: Cross multiply
    7,702x = 12,403 × 12,403
  4. Step 4: Simplify right side
    7,702x = 153,834,409
  5. Step 5: Solve for x
    x = 153,834,409/7,702
  6. Step 6: Final answer
    x = 19,973.31

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.