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Finding the Third Proportional to 51,214 and 106,516

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Solution

The third proportional to 51,214 and 106,516 is: 221,534.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,214 : 106,516 = 106,516 : x
  2. Step 2: Convert to fraction form
    51,214/106,516 = 106,516/x
  3. Step 3: Cross multiply
    51,214x = 106,516 × 106,516
  4. Step 4: Simplify right side
    51,214x = 11,345,658,256
  5. Step 5: Solve for x
    x = 11,345,658,256/51,214
  6. Step 6: Final answer
    x = 221,534.31

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Why These Related Problems?

These problems maintain the same ratio (2.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.