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Finding the Third Proportional to 77,824 and 172,032

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Solution

The third proportional to 77,824 and 172,032 is: 380,281.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    77,824 : 172,032 = 172,032 : x
  2. Step 2: Convert to fraction form
    77,824/172,032 = 172,032/x
  3. Step 3: Cross multiply
    77,824x = 172,032 × 172,032
  4. Step 4: Simplify right side
    77,824x = 29,595,009,024
  5. Step 5: Solve for x
    x = 29,595,009,024/77,824
  6. Step 6: Final answer
    x = 380,281.26

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Why These Related Problems?

These problems maintain the same ratio (2.21) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.