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Finding the Third Proportional to 32,178 and 49,824

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Solution

The third proportional to 32,178 and 49,824 is: 77,146.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    32,178 : 49,824 = 49,824 : x
  2. Step 2: Convert to fraction form
    32,178/49,824 = 49,824/x
  3. Step 3: Cross multiply
    32,178x = 49,824 × 49,824
  4. Step 4: Simplify right side
    32,178x = 2,482,430,976
  5. Step 5: Solve for x
    x = 2,482,430,976/32,178
  6. Step 6: Final answer
    x = 77,146.84

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Why These Related Problems?

These problems maintain the same ratio (1.55) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.