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Finding the Third Proportional to 51,776 and 77,582

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Solution

The third proportional to 51,776 and 77,582 is: 116,250.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    51,776 : 77,582 = 77,582 : x
  2. Step 2: Convert to fraction form
    51,776/77,582 = 77,582/x
  3. Step 3: Cross multiply
    51,776x = 77,582 × 77,582
  4. Step 4: Simplify right side
    51,776x = 6,018,966,724
  5. Step 5: Solve for x
    x = 6,018,966,724/51,776
  6. Step 6: Final answer
    x = 116,250.13

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.