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Finding the Third Proportional to 5,638 and 8,411

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Solution

The third proportional to 5,638 and 8,411 is: 12,547.88

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,638 : 8,411 = 8,411 : x
  2. Step 2: Convert to fraction form
    5,638/8,411 = 8,411/x
  3. Step 3: Cross multiply
    5,638x = 8,411 × 8,411
  4. Step 4: Simplify right side
    5,638x = 70,744,921
  5. Step 5: Solve for x
    x = 70,744,921/5,638
  6. Step 6: Final answer
    x = 12,547.88

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Why These Related Problems?

These problems maintain the same ratio (1.49) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.