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Finding the Third Proportional to 14,541 and 31,407

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Solution

The third proportional to 14,541 and 31,407 is: 67,835.75

Step by Step Solution

  1. Step 1: Write the proportion equation
    14,541 : 31,407 = 31,407 : x
  2. Step 2: Convert to fraction form
    14,541/31,407 = 31,407/x
  3. Step 3: Cross multiply
    14,541x = 31,407 × 31,407
  4. Step 4: Simplify right side
    14,541x = 986,399,649
  5. Step 5: Solve for x
    x = 986,399,649/14,541
  6. Step 6: Final answer
    x = 67,835.75

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.