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Finding the Third Proportional to 4,202 and 9,737

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Solution

The third proportional to 4,202 and 9,737 is: 22,562.87

Step by Step Solution

  1. Step 1: Write the proportion equation
    4,202 : 9,737 = 9,737 : x
  2. Step 2: Convert to fraction form
    4,202/9,737 = 9,737/x
  3. Step 3: Cross multiply
    4,202x = 9,737 × 9,737
  4. Step 4: Simplify right side
    4,202x = 94,809,169
  5. Step 5: Solve for x
    x = 94,809,169/4,202
  6. Step 6: Final answer
    x = 22,562.87

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Why These Related Problems?

These problems maintain the same ratio (2.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.