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Finding the Third Proportional to 7,642 and 8,434

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Solution

The third proportional to 7,642 and 8,434 is: 9,308.08

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,642 : 8,434 = 8,434 : x
  2. Step 2: Convert to fraction form
    7,642/8,434 = 8,434/x
  3. Step 3: Cross multiply
    7,642x = 8,434 × 8,434
  4. Step 4: Simplify right side
    7,642x = 71,132,356
  5. Step 5: Solve for x
    x = 71,132,356/7,642
  6. Step 6: Final answer
    x = 9,308.08

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.