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Finding the Third Proportional to 7,714 and 8,524

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Solution

The third proportional to 7,714 and 8,524 is: 9,419.05

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,714 : 8,524 = 8,524 : x
  2. Step 2: Convert to fraction form
    7,714/8,524 = 8,524/x
  3. Step 3: Cross multiply
    7,714x = 8,524 × 8,524
  4. Step 4: Simplify right side
    7,714x = 72,658,576
  5. Step 5: Solve for x
    x = 72,658,576/7,714
  6. Step 6: Final answer
    x = 9,419.05

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Why These Related Problems?

These problems maintain the same ratio (1.11) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.