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Finding the Third Proportional to 59,049 and 129,033

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Solution

The third proportional to 59,049 and 129,033 is: 281,961

Step by Step Solution

  1. Step 1: Write the proportion equation
    59,049 : 129,033 = 129,033 : x
  2. Step 2: Convert to fraction form
    59,049/129,033 = 129,033/x
  3. Step 3: Cross multiply
    59,049x = 129,033 × 129,033
  4. Step 4: Simplify right side
    59,049x = 16,649,515,089
  5. Step 5: Solve for x
    x = 16,649,515,089/59,049
  6. Step 6: Final answer
    x = 281,961

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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.