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Finding the Third Proportional to 7,822 and 15,854

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Solution

The third proportional to 7,822 and 15,854 is: 32,133.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,822 : 15,854 = 15,854 : x
  2. Step 2: Convert to fraction form
    7,822/15,854 = 15,854/x
  3. Step 3: Cross multiply
    7,822x = 15,854 × 15,854
  4. Step 4: Simplify right side
    7,822x = 251,349,316
  5. Step 5: Solve for x
    x = 251,349,316/7,822
  6. Step 6: Final answer
    x = 32,133.64

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Why These Related Problems?

These problems maintain the same ratio (2.03) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.