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Finding the Third Proportional to 29,965 and 65,213

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Solution

The third proportional to 29,965 and 65,213 is: 141,923.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    29,965 : 65,213 = 65,213 : x
  2. Step 2: Convert to fraction form
    29,965/65,213 = 65,213/x
  3. Step 3: Cross multiply
    29,965x = 65,213 × 65,213
  4. Step 4: Simplify right side
    29,965x = 4,252,735,369
  5. Step 5: Solve for x
    x = 4,252,735,369/29,965
  6. Step 6: Final answer
    x = 141,923.42

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.