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Finding the Third Proportional to 77,784 and 169,824

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Solution

The third proportional to 77,784 and 169,824 is: 370,772.79

Step by Step Solution

  1. Step 1: Write the proportion equation
    77,784 : 169,824 = 169,824 : x
  2. Step 2: Convert to fraction form
    77,784/169,824 = 169,824/x
  3. Step 3: Cross multiply
    77,784x = 169,824 × 169,824
  4. Step 4: Simplify right side
    77,784x = 28,840,190,976
  5. Step 5: Solve for x
    x = 28,840,190,976/77,784
  6. Step 6: Final answer
    x = 370,772.79

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Why These Related Problems?

These problems maintain the same ratio (2.18) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.