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Finding the Third Proportional to 180,400 and 385,824

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Solution

The third proportional to 180,400 and 385,824 is: 825,167.18

Step by Step Solution

  1. Step 1: Write the proportion equation
    180,400 : 385,824 = 385,824 : x
  2. Step 2: Convert to fraction form
    180,400/385,824 = 385,824/x
  3. Step 3: Cross multiply
    180,400x = 385,824 × 385,824
  4. Step 4: Simplify right side
    180,400x = 148,860,158,976
  5. Step 5: Solve for x
    x = 148,860,158,976/180,400
  6. Step 6: Final answer
    x = 825,167.18

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.