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Finding the Third Proportional to 106,824 and 233,498

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Solution

The third proportional to 106,824 and 233,498 is: 510,384.52

Step by Step Solution

  1. Step 1: Write the proportion equation
    106,824 : 233,498 = 233,498 : x
  2. Step 2: Convert to fraction form
    106,824/233,498 = 233,498/x
  3. Step 3: Cross multiply
    106,824x = 233,498 × 233,498
  4. Step 4: Simplify right side
    106,824x = 54,521,316,004
  5. Step 5: Solve for x
    x = 54,521,316,004/106,824
  6. Step 6: Final answer
    x = 510,384.52

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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.