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Finding the Third Proportional to 7,709 and 8,429

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Solution

The third proportional to 7,709 and 8,429 is: 9,216.25

Step by Step Solution

  1. Step 1: Write the proportion equation
    7,709 : 8,429 = 8,429 : x
  2. Step 2: Convert to fraction form
    7,709/8,429 = 8,429/x
  3. Step 3: Cross multiply
    7,709x = 8,429 × 8,429
  4. Step 4: Simplify right side
    7,709x = 71,048,041
  5. Step 5: Solve for x
    x = 71,048,041/7,709
  6. Step 6: Final answer
    x = 9,216.25

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.