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Finding the Third Proportional to 51,696 and 77,976

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Solution

The third proportional to 51,696 and 77,976 is: 117,615.61

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,696 : 77,976 = 77,976 : x
  2. Step 2: Convert to fraction form
    51,696/77,976 = 77,976/x
  3. Step 3: Cross multiply
    51,696x = 77,976 × 77,976
  4. Step 4: Simplify right side
    51,696x = 6,080,256,576
  5. Step 5: Solve for x
    x = 6,080,256,576/51,696
  6. Step 6: Final answer
    x = 117,615.61

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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.