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Finding the Third Proportional to 2,972 and 6,511

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Solution

The third proportional to 2,972 and 6,511 is: 14,264.17

Step by Step Solution

  1. Step 1: Write the proportion equation
    2,972 : 6,511 = 6,511 : x
  2. Step 2: Convert to fraction form
    2,972/6,511 = 6,511/x
  3. Step 3: Cross multiply
    2,972x = 6,511 × 6,511
  4. Step 4: Simplify right side
    2,972x = 42,393,121
  5. Step 5: Solve for x
    x = 42,393,121/2,972
  6. Step 6: Final answer
    x = 14,264.17

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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.