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Finding the Third Proportional to 15,824 and 22,496

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Solution

The third proportional to 15,824 and 22,496 is: 31,981.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    15,824 : 22,496 = 22,496 : x
  2. Step 2: Convert to fraction form
    15,824/22,496 = 22,496/x
  3. Step 3: Cross multiply
    15,824x = 22,496 × 22,496
  4. Step 4: Simplify right side
    15,824x = 506,070,016
  5. Step 5: Solve for x
    x = 506,070,016/15,824
  6. Step 6: Final answer
    x = 31,981.17

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Why These Related Problems?

These problems maintain the same ratio (1.42) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.