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Finding the Third Proportional to 2,076 and 4,210

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Solution

The third proportional to 2,076 and 4,210 is: 8,537.62

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,076 : 4,210 = 4,210 : x
  2. Step 2: Convert to fraction form
    2,076/4,210 = 4,210/x
  3. Step 3: Cross multiply
    2,076x = 4,210 × 4,210
  4. Step 4: Simplify right side
    2,076x = 17,724,100
  5. Step 5: Solve for x
    x = 17,724,100/2,076
  6. Step 6: Final answer
    x = 8,537.62

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Why These Related Problems?

These problems maintain the same ratio (2.03) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.