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Finding the Third Proportional to 6,998 and 8,210

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Solution

The third proportional to 6,998 and 8,210 is: 9,631.91

Step by Step Solution

  1. Step 1: Write the proportion equation
    6,998 : 8,210 = 8,210 : x
  2. Step 2: Convert to fraction form
    6,998/8,210 = 8,210/x
  3. Step 3: Cross multiply
    6,998x = 8,210 × 8,210
  4. Step 4: Simplify right side
    6,998x = 67,404,100
  5. Step 5: Solve for x
    x = 67,404,100/6,998
  6. Step 6: Final answer
    x = 9,631.91

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Why These Related Problems?

These problems maintain the same ratio (1.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.