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Finding the Third Proportional to 51,823 and 80,024

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Solution

The third proportional to 51,823 and 80,024 is: 123,571.40

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,823 : 80,024 = 80,024 : x
  2. Step 2: Convert to fraction form
    51,823/80,024 = 80,024/x
  3. Step 3: Cross multiply
    51,823x = 80,024 × 80,024
  4. Step 4: Simplify right side
    51,823x = 6,403,840,576
  5. Step 5: Solve for x
    x = 6,403,840,576/51,823
  6. Step 6: Final answer
    x = 123,571.40

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.