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Finding the Third Proportional to 678.50 and 982.50

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Solution

The third proportional to 678.50 and 982.50 is: 1,422.71

Step by Step Solution

  1. Step 1: Write the proportion equation
    678.50 : 982.50 = 982.50 : x
  2. Step 2: Convert to fraction form
    678.50/982.50 = 982.50/x
  3. Step 3: Cross multiply
    678.50x = 982.50 × 982.50
  4. Step 4: Simplify right side
    678.50x = 965,306.25
  5. Step 5: Solve for x
    x = 965,306.25/678.50
  6. Step 6: Final answer
    x = 1,422.71

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Why These Related Problems?

These problems maintain the same ratio (1.45) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.