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Finding the Third Proportional to 31,830 and 67,998

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Solution

The third proportional to 31,830 and 67,998 is: 145,263.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    31,830 : 67,998 = 67,998 : x
  2. Step 2: Convert to fraction form
    31,830/67,998 = 67,998/x
  3. Step 3: Cross multiply
    31,830x = 67,998 × 67,998
  4. Step 4: Simplify right side
    31,830x = 4,623,728,004
  5. Step 5: Solve for x
    x = 4,623,728,004/31,830
  6. Step 6: Final answer
    x = 145,263.21

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.