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Finding the Third Proportional to 10,824 and 16,354

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Solution

The third proportional to 10,824 and 16,354 is: 24,709.29

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,824 : 16,354 = 16,354 : x
  2. Step 2: Convert to fraction form
    10,824/16,354 = 16,354/x
  3. Step 3: Cross multiply
    10,824x = 16,354 × 16,354
  4. Step 4: Simplify right side
    10,824x = 267,453,316
  5. Step 5: Solve for x
    x = 267,453,316/10,824
  6. Step 6: Final answer
    x = 24,709.29

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.