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Finding the Third Proportional to 76,534 and 102,651

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Solution

The third proportional to 76,534 and 102,651 is: 137,680.35

Step by Step Solution

  1. Step 1: Write the proportion equation
    76,534 : 102,651 = 102,651 : x
  2. Step 2: Convert to fraction form
    76,534/102,651 = 102,651/x
  3. Step 3: Cross multiply
    76,534x = 102,651 × 102,651
  4. Step 4: Simplify right side
    76,534x = 10,537,227,801
  5. Step 5: Solve for x
    x = 10,537,227,801/76,534
  6. Step 6: Final answer
    x = 137,680.35

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Why These Related Problems?

These problems maintain the same ratio (1.34) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.