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Finding the Third Proportional to 4,213 and 9,970

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Solution

The third proportional to 4,213 and 9,970 is: 23,593.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,213 : 9,970 = 9,970 : x
  2. Step 2: Convert to fraction form
    4,213/9,970 = 9,970/x
  3. Step 3: Cross multiply
    4,213x = 9,970 × 9,970
  4. Step 4: Simplify right side
    4,213x = 99,400,900
  5. Step 5: Solve for x
    x = 99,400,900/4,213
  6. Step 6: Final answer
    x = 23,593.85

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Why These Related Problems?

These problems maintain the same ratio (2.37) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.