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Finding the Third Proportional to 213,048 and 456,023

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Solution

The third proportional to 213,048 and 456,023 is: 976,103.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    213,048 : 456,023 = 456,023 : x
  2. Step 2: Convert to fraction form
    213,048/456,023 = 456,023/x
  3. Step 3: Cross multiply
    213,048x = 456,023 × 456,023
  4. Step 4: Simplify right side
    213,048x = 207,956,976,529
  5. Step 5: Solve for x
    x = 207,956,976,529/213,048
  6. Step 6: Final answer
    x = 976,103.87

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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.