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Finding the Third Proportional to 5,641 and 12,409

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Solution

The third proportional to 5,641 and 12,409 is: 27,297.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,641 : 12,409 = 12,409 : x
  2. Step 2: Convert to fraction form
    5,641/12,409 = 12,409/x
  3. Step 3: Cross multiply
    5,641x = 12,409 × 12,409
  4. Step 4: Simplify right side
    5,641x = 153,983,281
  5. Step 5: Solve for x
    x = 153,983,281/5,641
  6. Step 6: Final answer
    x = 27,297.16

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Why These Related Problems?

These problems maintain the same ratio (2.20) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.