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Finding the Third Proportional to 105,408 and 165,024

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Solution

The third proportional to 105,408 and 165,024 is: 258,357.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    105,408 : 165,024 = 165,024 : x
  2. Step 2: Convert to fraction form
    105,408/165,024 = 165,024/x
  3. Step 3: Cross multiply
    105,408x = 165,024 × 165,024
  4. Step 4: Simplify right side
    105,408x = 27,232,920,576
  5. Step 5: Solve for x
    x = 27,232,920,576/105,408
  6. Step 6: Final answer
    x = 258,357.25

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Why These Related Problems?

These problems maintain the same ratio (1.57) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.