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Finding the Third Proportional to 2,138 and 3,430

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Solution

The third proportional to 2,138 and 3,430 is: 5,502.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,138 : 3,430 = 3,430 : x
  2. Step 2: Convert to fraction form
    2,138/3,430 = 3,430/x
  3. Step 3: Cross multiply
    2,138x = 3,430 × 3,430
  4. Step 4: Simplify right side
    2,138x = 11,764,900
  5. Step 5: Solve for x
    x = 11,764,900/2,138
  6. Step 6: Final answer
    x = 5,502.76

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Why These Related Problems?

These problems maintain the same ratio (1.60) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.