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Finding the Third Proportional to 5,146 and 6,502

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Solution

The third proportional to 5,146 and 6,502 is: 8,215.31

Step by Step Solution

  1. Step 1: Write the proportion equation
    5,146 : 6,502 = 6,502 : x
  2. Step 2: Convert to fraction form
    5,146/6,502 = 6,502/x
  3. Step 3: Cross multiply
    5,146x = 6,502 × 6,502
  4. Step 4: Simplify right side
    5,146x = 42,276,004
  5. Step 5: Solve for x
    x = 42,276,004/5,146
  6. Step 6: Final answer
    x = 8,215.31

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Why These Related Problems?

These problems maintain the same ratio (1.26) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.