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Finding the Third Proportional to 1,650 and 2,709

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Solution

The third proportional to 1,650 and 2,709 is: 4,447.69

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,650 : 2,709 = 2,709 : x
  2. Step 2: Convert to fraction form
    1,650/2,709 = 2,709/x
  3. Step 3: Cross multiply
    1,650x = 2,709 × 2,709
  4. Step 4: Simplify right side
    1,650x = 7,338,681
  5. Step 5: Solve for x
    x = 7,338,681/1,650
  6. Step 6: Final answer
    x = 4,447.69

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Why These Related Problems?

These problems maintain the same ratio (1.64) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.