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Finding the Third Proportional to 972 and 2,006

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Solution

The third proportional to 972 and 2,006 is: 4,139.95

Step by Step Solution

  1. Step 1: Write the proportion equation
    972 : 2,006 = 2,006 : x
  2. Step 2: Convert to fraction form
    972/2,006 = 2,006/x
  3. Step 3: Cross multiply
    972x = 2,006 × 2,006
  4. Step 4: Simplify right side
    972x = 4,024,036
  5. Step 5: Solve for x
    x = 4,024,036/972
  6. Step 6: Final answer
    x = 4,139.95

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Why These Related Problems?

These problems maintain the same ratio (2.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.