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Finding the Third Proportional to 1,538 and 2,309

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Solution

The third proportional to 1,538 and 2,309 is: 3,466.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,538 : 2,309 = 2,309 : x
  2. Step 2: Convert to fraction form
    1,538/2,309 = 2,309/x
  3. Step 3: Cross multiply
    1,538x = 2,309 × 2,309
  4. Step 4: Simplify right side
    1,538x = 5,331,481
  5. Step 5: Solve for x
    x = 5,331,481/1,538
  6. Step 6: Final answer
    x = 3,466.50

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Why These Related Problems?

These problems maintain the same ratio (1.50) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.