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Finding the Third Proportional to 100,033 and 213,458

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Solution

The third proportional to 100,033 and 213,458 is: 455,492.86

Step by Step Solution

  1. Step 1: Write the proportion equation
    100,033 : 213,458 = 213,458 : x
  2. Step 2: Convert to fraction form
    100,033/213,458 = 213,458/x
  3. Step 3: Cross multiply
    100,033x = 213,458 × 213,458
  4. Step 4: Simplify right side
    100,033x = 45,564,317,764
  5. Step 5: Solve for x
    x = 45,564,317,764/100,033
  6. Step 6: Final answer
    x = 455,492.86

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Why These Related Problems?

These problems maintain the same ratio (2.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.