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Finding the Third Proportional to 6,980 and 9,784

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Solution

The third proportional to 6,980 and 9,784 is: 13,714.42

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,980 : 9,784 = 9,784 : x
  2. Step 2: Convert to fraction form
    6,980/9,784 = 9,784/x
  3. Step 3: Cross multiply
    6,980x = 9,784 × 9,784
  4. Step 4: Simplify right side
    6,980x = 95,726,656
  5. Step 5: Solve for x
    x = 95,726,656/6,980
  6. Step 6: Final answer
    x = 13,714.42

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.