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Finding the Third Proportional to 1,538 and 2,306.50

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Solution

The third proportional to 1,538 and 2,306.50 is: 3,459.00

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,538 : 2,306.50 = 2,306.50 : x
  2. Step 2: Convert to fraction form
    1,538/2,306.50 = 2,306.50/x
  3. Step 3: Cross multiply
    1,538x = 2,306.50 × 2,306.50
  4. Step 4: Simplify right side
    1,538x = 5,319,942.25
  5. Step 5: Solve for x
    x = 5,319,942.25/1,538
  6. Step 6: Final answer
    x = 3,459.00

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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.