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Finding the Third Proportional to 29,824 and 65,257

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Solution

The third proportional to 29,824 and 65,257 is: 142,786.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    29,824 : 65,257 = 65,257 : x
  2. Step 2: Convert to fraction form
    29,824/65,257 = 65,257/x
  3. Step 3: Cross multiply
    29,824x = 65,257 × 65,257
  4. Step 4: Simplify right side
    29,824x = 4,258,476,049
  5. Step 5: Solve for x
    x = 4,258,476,049/29,824
  6. Step 6: Final answer
    x = 142,786.88

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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.