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Finding the Third Proportional to 6,298 and 7,706

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Solution

The third proportional to 6,298 and 7,706 is: 9,428.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,298 : 7,706 = 7,706 : x
  2. Step 2: Convert to fraction form
    6,298/7,706 = 7,706/x
  3. Step 3: Cross multiply
    6,298x = 7,706 × 7,706
  4. Step 4: Simplify right side
    6,298x = 59,382,436
  5. Step 5: Solve for x
    x = 59,382,436/6,298
  6. Step 6: Final answer
    x = 9,428.78

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Why These Related Problems?

These problems maintain the same ratio (1.22) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.