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Finding the Third Proportional to 2,976 and 6,505

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Solution

The third proportional to 2,976 and 6,505 is: 14,218.76

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,976 : 6,505 = 6,505 : x
  2. Step 2: Convert to fraction form
    2,976/6,505 = 6,505/x
  3. Step 3: Cross multiply
    2,976x = 6,505 × 6,505
  4. Step 4: Simplify right side
    2,976x = 42,315,025
  5. Step 5: Solve for x
    x = 42,315,025/2,976
  6. Step 6: Final answer
    x = 14,218.76

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Why These Related Problems?

These problems maintain the same ratio (2.19) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.