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Finding the Third Proportional to 51,784 and 75,974

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Solution

The third proportional to 51,784 and 75,974 is: 111,463.94

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,784 : 75,974 = 75,974 : x
  2. Step 2: Convert to fraction form
    51,784/75,974 = 75,974/x
  3. Step 3: Cross multiply
    51,784x = 75,974 × 75,974
  4. Step 4: Simplify right side
    51,784x = 5,772,048,676
  5. Step 5: Solve for x
    x = 5,772,048,676/51,784
  6. Step 6: Final answer
    x = 111,463.94

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.