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Finding the Third Proportional to 10,314 and 15,822

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Solution

The third proportional to 10,314 and 15,822 is: 24,271.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    10,314 : 15,822 = 15,822 : x
  2. Step 2: Convert to fraction form
    10,314/15,822 = 15,822/x
  3. Step 3: Cross multiply
    10,314x = 15,822 × 15,822
  4. Step 4: Simplify right side
    10,314x = 250,335,684
  5. Step 5: Solve for x
    x = 250,335,684/10,314
  6. Step 6: Final answer
    x = 24,271.45

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Why These Related Problems?

These problems maintain the same ratio (1.53) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.