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Finding the Third Proportional to 10,822 and 13,306

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Solution

The third proportional to 10,822 and 13,306 is: 16,360.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,822 : 13,306 = 13,306 : x
  2. Step 2: Convert to fraction form
    10,822/13,306 = 13,306/x
  3. Step 3: Cross multiply
    10,822x = 13,306 × 13,306
  4. Step 4: Simplify right side
    10,822x = 177,049,636
  5. Step 5: Solve for x
    x = 177,049,636/10,822
  6. Step 6: Final answer
    x = 16,360.16

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Why These Related Problems?

These problems maintain the same ratio (1.23) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.