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Finding the Third Proportional to 4,106 and 8,454

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Solution

The third proportional to 4,106 and 8,454 is: 17,406.26

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,106 : 8,454 = 8,454 : x
  2. Step 2: Convert to fraction form
    4,106/8,454 = 8,454/x
  3. Step 3: Cross multiply
    4,106x = 8,454 × 8,454
  4. Step 4: Simplify right side
    4,106x = 71,470,116
  5. Step 5: Solve for x
    x = 71,470,116/4,106
  6. Step 6: Final answer
    x = 17,406.26

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Why These Related Problems?

These problems maintain the same ratio (2.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.