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Finding the Third Proportional to 709.75 and 1,096.25

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Solution

The third proportional to 709.75 and 1,096.25 is: 1,693.22

Step by Step Solution

  1. Step 1: Write the proportion equation
    709.75 : 1,096.25 = 1,096.25 : x
  2. Step 2: Convert to fraction form
    709.75/1,096.25 = 1,096.25/x
  3. Step 3: Cross multiply
    709.75x = 1,096.25 × 1,096.25
  4. Step 4: Simplify right side
    709.75x = 1,201,764.06
  5. Step 5: Solve for x
    x = 1,201,764.06/709.75
  6. Step 6: Final answer
    x = 1,693.22

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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.