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Finding the Third Proportional to 51,784 and 110,946

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Solution

The third proportional to 51,784 and 110,946 is: 237,699.19

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,784 : 110,946 = 110,946 : x
  2. Step 2: Convert to fraction form
    51,784/110,946 = 110,946/x
  3. Step 3: Cross multiply
    51,784x = 110,946 × 110,946
  4. Step 4: Simplify right side
    51,784x = 12,309,014,916
  5. Step 5: Solve for x
    x = 12,309,014,916/51,784
  6. Step 6: Final answer
    x = 237,699.19

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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.