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Finding the Third Proportional to 1,648 and 3,642

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Solution

The third proportional to 1,648 and 3,642 is: 8,048.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,648 : 3,642 = 3,642 : x
  2. Step 2: Convert to fraction form
    1,648/3,642 = 3,642/x
  3. Step 3: Cross multiply
    1,648x = 3,642 × 3,642
  4. Step 4: Simplify right side
    1,648x = 13,264,164
  5. Step 5: Solve for x
    x = 13,264,164/1,648
  6. Step 6: Final answer
    x = 8,048.64

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Why These Related Problems?

These problems maintain the same ratio (2.21) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.