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Finding the Third Proportional to 5,192 and 5,896

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Solution

The third proportional to 5,192 and 5,896 is: 6,695.46

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,192 : 5,896 = 5,896 : x
  2. Step 2: Convert to fraction form
    5,192/5,896 = 5,896/x
  3. Step 3: Cross multiply
    5,192x = 5,896 × 5,896
  4. Step 4: Simplify right side
    5,192x = 34,762,816
  5. Step 5: Solve for x
    x = 34,762,816/5,192
  6. Step 6: Final answer
    x = 6,695.46

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Why These Related Problems?

These problems maintain the same ratio (1.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.