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Finding the Third Proportional to 706 and 1,069

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Solution

The third proportional to 706 and 1,069 is: 1,618.64

Step by Step Solution

  1. Step 1: Write the proportion equation
    706 : 1,069 = 1,069 : x
  2. Step 2: Convert to fraction form
    706/1,069 = 1,069/x
  3. Step 3: Cross multiply
    706x = 1,069 × 1,069
  4. Step 4: Simplify right side
    706x = 1,142,761
  5. Step 5: Solve for x
    x = 1,142,761/706
  6. Step 6: Final answer
    x = 1,618.64

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Why These Related Problems?

These problems maintain the same ratio (1.51) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.