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Finding the Third Proportional to 5,138 and 5,642

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Solution

The third proportional to 5,138 and 5,642 is: 6,195.44

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,138 : 5,642 = 5,642 : x
  2. Step 2: Convert to fraction form
    5,138/5,642 = 5,642/x
  3. Step 3: Cross multiply
    5,138x = 5,642 × 5,642
  4. Step 4: Simplify right side
    5,138x = 31,832,164
  5. Step 5: Solve for x
    x = 31,832,164/5,138
  6. Step 6: Final answer
    x = 6,195.44

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.