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Finding the Third Proportional to 4,210 and 7,812

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Solution

The third proportional to 4,210 and 7,812 is: 14,495.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,210 : 7,812 = 7,812 : x
  2. Step 2: Convert to fraction form
    4,210/7,812 = 7,812/x
  3. Step 3: Cross multiply
    4,210x = 7,812 × 7,812
  4. Step 4: Simplify right side
    4,210x = 61,027,344
  5. Step 5: Solve for x
    x = 61,027,344/4,210
  6. Step 6: Final answer
    x = 14,495.81

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Why These Related Problems?

These problems maintain the same ratio (1.86) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.