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Finding the Third Proportional to 4,206 and 4,770

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Solution

The third proportional to 4,206 and 4,770 is: 5,409.63

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,206 : 4,770 = 4,770 : x
  2. Step 2: Convert to fraction form
    4,206/4,770 = 4,770/x
  3. Step 3: Cross multiply
    4,206x = 4,770 × 4,770
  4. Step 4: Simplify right side
    4,206x = 22,752,900
  5. Step 5: Solve for x
    x = 22,752,900/4,206
  6. Step 6: Final answer
    x = 5,409.63

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Why These Related Problems?

These problems maintain the same ratio (1.13) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.