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Finding the Third Proportional to 13,096 and 14,216

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Solution

The third proportional to 13,096 and 14,216 is: 15,431.78

Step by Step Solution

  1. Step 1: Write the proportion equation
    13,096 : 14,216 = 14,216 : x
  2. Step 2: Convert to fraction form
    13,096/14,216 = 14,216/x
  3. Step 3: Cross multiply
    13,096x = 14,216 × 14,216
  4. Step 4: Simplify right side
    13,096x = 202,094,656
  5. Step 5: Solve for x
    x = 202,094,656/13,096
  6. Step 6: Final answer
    x = 15,431.78

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Why These Related Problems?

These problems maintain the same ratio (1.09) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.