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Finding the Third Proportional to 121,296 and 177,984

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Solution

The third proportional to 121,296 and 177,984 is: 261,165.28

Step by Step Solution

  1. Step 1: Write the proportion equation
    121,296 : 177,984 = 177,984 : x
  2. Step 2: Convert to fraction form
    121,296/177,984 = 177,984/x
  3. Step 3: Cross multiply
    121,296x = 177,984 × 177,984
  4. Step 4: Simplify right side
    121,296x = 31,678,304,256
  5. Step 5: Solve for x
    x = 31,678,304,256/121,296
  6. Step 6: Final answer
    x = 261,165.28

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.