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Finding the Third Proportional to 3,830 and 4,190

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Solution

The third proportional to 3,830 and 4,190 is: 4,583.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,830 : 4,190 = 4,190 : x
  2. Step 2: Convert to fraction form
    3,830/4,190 = 4,190/x
  3. Step 3: Cross multiply
    3,830x = 4,190 × 4,190
  4. Step 4: Simplify right side
    3,830x = 17,556,100
  5. Step 5: Solve for x
    x = 17,556,100/3,830
  6. Step 6: Final answer
    x = 4,583.84

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.