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Finding the Third Proportional to 24,409 and 53,489

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Solution

The third proportional to 24,409 and 53,489 is: 117,213.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    24,409 : 53,489 = 53,489 : x
  2. Step 2: Convert to fraction form
    24,409/53,489 = 53,489/x
  3. Step 3: Cross multiply
    24,409x = 53,489 × 53,489
  4. Step 4: Simplify right side
    24,409x = 2,861,073,121
  5. Step 5: Solve for x
    x = 2,861,073,121/24,409
  6. Step 6: Final answer
    x = 117,213.86

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.