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Finding the Third Proportional to 51,649 and 109,498

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Solution

The third proportional to 51,649 and 109,498 is: 232,140.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,649 : 109,498 = 109,498 : x
  2. Step 2: Convert to fraction form
    51,649/109,498 = 109,498/x
  3. Step 3: Cross multiply
    51,649x = 109,498 × 109,498
  4. Step 4: Simplify right side
    51,649x = 11,989,812,004
  5. Step 5: Solve for x
    x = 11,989,812,004/51,649
  6. Step 6: Final answer
    x = 232,140.25

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Why These Related Problems?

These problems maintain the same ratio (2.12) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.