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Finding the Third Proportional to 678 and 729.75

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Solution

The third proportional to 678 and 729.75 is: 785.45

Step by Step Solution

  1. Step 1: Write the proportion equation
    678 : 729.75 = 729.75 : x
  2. Step 2: Convert to fraction form
    678/729.75 = 729.75/x
  3. Step 3: Cross multiply
    678x = 729.75 × 729.75
  4. Step 4: Simplify right side
    678x = 532,535.06
  5. Step 5: Solve for x
    x = 532,535.06/678
  6. Step 6: Final answer
    x = 785.45

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Why These Related Problems?

These problems maintain the same ratio (1.08) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.