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Finding the Third Proportional to 24,970 and 53,824

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Solution

The third proportional to 24,970 and 53,824 is: 116,020.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    24,970 : 53,824 = 53,824 : x
  2. Step 2: Convert to fraction form
    24,970/53,824 = 53,824/x
  3. Step 3: Cross multiply
    24,970x = 53,824 × 53,824
  4. Step 4: Simplify right side
    24,970x = 2,897,022,976
  5. Step 5: Solve for x
    x = 2,897,022,976/24,970
  6. Step 6: Final answer
    x = 116,020.14

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Why These Related Problems?

These problems maintain the same ratio (2.16) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.