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Finding the Third Proportional to 1,576 and 3,698

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Solution

The third proportional to 1,576 and 3,698 is: 8,677.16

Step by Step Solution

  1. Step 1: Write the proportion equation
    1,576 : 3,698 = 3,698 : x
  2. Step 2: Convert to fraction form
    1,576/3,698 = 3,698/x
  3. Step 3: Cross multiply
    1,576x = 3,698 × 3,698
  4. Step 4: Simplify right side
    1,576x = 13,675,204
  5. Step 5: Solve for x
    x = 13,675,204/1,576
  6. Step 6: Final answer
    x = 8,677.16

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Why These Related Problems?

These problems maintain the same ratio (2.35) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.