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Finding the Third Proportional to 29,971 and 65,774

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Solution

The third proportional to 29,971 and 65,774 is: 144,346.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    29,971 : 65,774 = 65,774 : x
  2. Step 2: Convert to fraction form
    29,971/65,774 = 65,774/x
  3. Step 3: Cross multiply
    29,971x = 65,774 × 65,774
  4. Step 4: Simplify right side
    29,971x = 4,326,219,076
  5. Step 5: Solve for x
    x = 4,326,219,076/29,971
  6. Step 6: Final answer
    x = 144,346.84

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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.