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Finding the Third Proportional to 3,870 and 4,210

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Solution

The third proportional to 3,870 and 4,210 is: 4,579.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    3,870 : 4,210 = 4,210 : x
  2. Step 2: Convert to fraction form
    3,870/4,210 = 4,210/x
  3. Step 3: Cross multiply
    3,870x = 4,210 × 4,210
  4. Step 4: Simplify right side
    3,870x = 17,724,100
  5. Step 5: Solve for x
    x = 17,724,100/3,870
  6. Step 6: Final answer
    x = 4,579.87

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.