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Finding the Third Proportional to 233,742 and 511,977

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Solution

The third proportional to 233,742 and 511,977 is: 1,121,409.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    233,742 : 511,977 = 511,977 : x
  2. Step 2: Convert to fraction form
    233,742/511,977 = 511,977/x
  3. Step 3: Cross multiply
    233,742x = 511,977 × 511,977
  4. Step 4: Simplify right side
    233,742x = 262,120,448,529
  5. Step 5: Solve for x
    x = 262,120,448,529/233,742
  6. Step 6: Final answer
    x = 1,121,409.28

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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.