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Finding the Third Proportional to 5,896 and 10,416

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Solution

The third proportional to 5,896 and 10,416 is: 18,401.13

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,896 : 10,416 = 10,416 : x
  2. Step 2: Convert to fraction form
    5,896/10,416 = 10,416/x
  3. Step 3: Cross multiply
    5,896x = 10,416 × 10,416
  4. Step 4: Simplify right side
    5,896x = 108,493,056
  5. Step 5: Solve for x
    x = 108,493,056/5,896
  6. Step 6: Final answer
    x = 18,401.13

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Why These Related Problems?

These problems maintain the same ratio (1.77) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.