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Finding the Third Proportional to 233,046 and 257,670

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Solution

The third proportional to 233,046 and 257,670 is: 284,895.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    233,046 : 257,670 = 257,670 : x
  2. Step 2: Convert to fraction form
    233,046/257,670 = 257,670/x
  3. Step 3: Cross multiply
    233,046x = 257,670 × 257,670
  4. Step 4: Simplify right side
    233,046x = 66,393,828,900
  5. Step 5: Solve for x
    x = 66,393,828,900/233,046
  6. Step 6: Final answer
    x = 284,895.81

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Why These Related Problems?

These problems maintain the same ratio (1.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.