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Finding the Third Proportional to 51,700 and 77,982

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Solution

The third proportional to 51,700 and 77,982 is: 117,624.61

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,700 : 77,982 = 77,982 : x
  2. Step 2: Convert to fraction form
    51,700/77,982 = 77,982/x
  3. Step 3: Cross multiply
    51,700x = 77,982 × 77,982
  4. Step 4: Simplify right side
    51,700x = 6,081,192,324
  5. Step 5: Solve for x
    x = 6,081,192,324/51,700
  6. Step 6: Final answer
    x = 117,624.61

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.