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Finding the Third Proportional to 106,357 and 232,033

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Solution

The third proportional to 106,357 and 232,033 is: 506,213.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    106,357 : 232,033 = 232,033 : x
  2. Step 2: Convert to fraction form
    106,357/232,033 = 232,033/x
  3. Step 3: Cross multiply
    106,357x = 232,033 × 232,033
  4. Step 4: Simplify right side
    106,357x = 53,839,313,089
  5. Step 5: Solve for x
    x = 53,839,313,089/106,357
  6. Step 6: Final answer
    x = 506,213.16

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.