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Finding the Third Proportional to 1,830 and 3,964

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Solution

The third proportional to 1,830 and 3,964 is: 8,586.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,830 : 3,964 = 3,964 : x
  2. Step 2: Convert to fraction form
    1,830/3,964 = 3,964/x
  3. Step 3: Cross multiply
    1,830x = 3,964 × 3,964
  4. Step 4: Simplify right side
    1,830x = 15,713,296
  5. Step 5: Solve for x
    x = 15,713,296/1,830
  6. Step 6: Final answer
    x = 8,586.50

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Why These Related Problems?

These problems maintain the same ratio (2.17) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.