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Finding the Third Proportional to 10,224 and 15,824

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Solution

The third proportional to 10,224 and 15,824 is: 24,491.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,224 : 15,824 = 15,824 : x
  2. Step 2: Convert to fraction form
    10,224/15,824 = 15,824/x
  3. Step 3: Cross multiply
    10,224x = 15,824 × 15,824
  4. Step 4: Simplify right side
    10,224x = 250,398,976
  5. Step 5: Solve for x
    x = 250,398,976/10,224
  6. Step 6: Final answer
    x = 24,491.29

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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.