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Finding the Third Proportional to 8,140 and 8,896

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Solution

The third proportional to 8,140 and 8,896 is: 9,722.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    8,140 : 8,896 = 8,896 : x
  2. Step 2: Convert to fraction form
    8,140/8,896 = 8,896/x
  3. Step 3: Cross multiply
    8,140x = 8,896 × 8,896
  4. Step 4: Simplify right side
    8,140x = 79,138,816
  5. Step 5: Solve for x
    x = 79,138,816/8,140
  6. Step 6: Final answer
    x = 9,722.21

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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.