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Finding the Third Proportional to 32,977 and 77,768

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Solution

The third proportional to 32,977 and 77,768 is: 183,396.36

Step by Step Solution

  1. Step 1: Write the proportion equation
    32,977 : 77,768 = 77,768 : x
  2. Step 2: Convert to fraction form
    32,977/77,768 = 77,768/x
  3. Step 3: Cross multiply
    32,977x = 77,768 × 77,768
  4. Step 4: Simplify right side
    32,977x = 6,047,861,824
  5. Step 5: Solve for x
    x = 6,047,861,824/32,977
  6. Step 6: Final answer
    x = 183,396.36

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Why These Related Problems?

These problems maintain the same ratio (2.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.