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Finding the Third Proportional to 1,650 and 4,002

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Solution

The third proportional to 1,650 and 4,002 is: 9,706.67

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,650 : 4,002 = 4,002 : x
  2. Step 2: Convert to fraction form
    1,650/4,002 = 4,002/x
  3. Step 3: Cross multiply
    1,650x = 4,002 × 4,002
  4. Step 4: Simplify right side
    1,650x = 16,016,004
  5. Step 5: Solve for x
    x = 16,016,004/1,650
  6. Step 6: Final answer
    x = 9,706.67

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Why These Related Problems?

These problems maintain the same ratio (2.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.