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Finding the Third Proportional to 7,702 and 12,242

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Solution

The third proportional to 7,702 and 12,242 is: 19,458.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,702 : 12,242 = 12,242 : x
  2. Step 2: Convert to fraction form
    7,702/12,242 = 12,242/x
  3. Step 3: Cross multiply
    7,702x = 12,242 × 12,242
  4. Step 4: Simplify right side
    7,702x = 149,866,564
  5. Step 5: Solve for x
    x = 149,866,564/7,702
  6. Step 6: Final answer
    x = 19,458.14

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Why These Related Problems?

These problems maintain the same ratio (1.59) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.