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Finding the Third Proportional to 13,824 and 21,312

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Solution

The third proportional to 13,824 and 21,312 is: 32,856

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,824 : 21,312 = 21,312 : x
  2. Step 2: Convert to fraction form
    13,824/21,312 = 21,312/x
  3. Step 3: Cross multiply
    13,824x = 21,312 × 21,312
  4. Step 4: Simplify right side
    13,824x = 454,201,344
  5. Step 5: Solve for x
    x = 454,201,344/13,824
  6. Step 6: Final answer
    x = 32,856

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.