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Finding the Third Proportional to 421.75 and 980.50

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Solution

The third proportional to 421.75 and 980.50 is: 2,279.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    421.75 : 980.50 = 980.50 : x
  2. Step 2: Convert to fraction form
    421.75/980.50 = 980.50/x
  3. Step 3: Cross multiply
    421.75x = 980.50 × 980.50
  4. Step 4: Simplify right side
    421.75x = 961,380.25
  5. Step 5: Solve for x
    x = 961,380.25/421.75
  6. Step 6: Final answer
    x = 2,279.50

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Why These Related Problems?

These problems maintain the same ratio (2.32) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.