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Finding the Third Proportional to 970 and 2,002

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Solution

The third proportional to 970 and 2,002 is: 4,131.96

Step by Step Solution

  1. Step 1: Write the proportion equation
    970 : 2,002 = 2,002 : x
  2. Step 2: Convert to fraction form
    970/2,002 = 2,002/x
  3. Step 3: Cross multiply
    970x = 2,002 × 2,002
  4. Step 4: Simplify right side
    970x = 4,008,004
  5. Step 5: Solve for x
    x = 4,008,004/970
  6. Step 6: Final answer
    x = 4,131.96

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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.