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Finding the Third Proportional to 709 and 1,091

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Solution

The third proportional to 709 and 1,091 is: 1,678.82

Step by Step Solution

  1. Step 1: Write the proportion equation
    709 : 1,091 = 1,091 : x
  2. Step 2: Convert to fraction form
    709/1,091 = 1,091/x
  3. Step 3: Cross multiply
    709x = 1,091 × 1,091
  4. Step 4: Simplify right side
    709x = 1,190,281
  5. Step 5: Solve for x
    x = 1,190,281/709
  6. Step 6: Final answer
    x = 1,678.82

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Why These Related Problems?

These problems maintain the same ratio (1.54) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.