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Finding the Third Proportional to 12,896 and 14,176

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Solution

The third proportional to 12,896 and 14,176 is: 15,583.05

Step by Step Solution

  1. Step 1: Write the proportion equation
    12,896 : 14,176 = 14,176 : x
  2. Step 2: Convert to fraction form
    12,896/14,176 = 14,176/x
  3. Step 3: Cross multiply
    12,896x = 14,176 × 14,176
  4. Step 4: Simplify right side
    12,896x = 200,958,976
  5. Step 5: Solve for x
    x = 200,958,976/12,896
  6. Step 6: Final answer
    x = 15,583.05

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Why These Related Problems?

These problems maintain the same ratio (1.10) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.