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Finding the Third Proportional to 4,212 and 8,154

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Solution

The third proportional to 4,212 and 8,154 is: 15,785.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,212 : 8,154 = 8,154 : x
  2. Step 2: Convert to fraction form
    4,212/8,154 = 8,154/x
  3. Step 3: Cross multiply
    4,212x = 8,154 × 8,154
  4. Step 4: Simplify right side
    4,212x = 66,487,716
  5. Step 5: Solve for x
    x = 66,487,716/4,212
  6. Step 6: Final answer
    x = 15,785.31

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Why These Related Problems?

These problems maintain the same ratio (1.94) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.