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Finding the Third Proportional to 289.50 and 420.75

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Solution

The third proportional to 289.50 and 420.75 is: 611.50

Step by Step Solution

  1. Step 1: Write the proportion equation
    289.50 : 420.75 = 420.75 : x
  2. Step 2: Convert to fraction form
    289.50/420.75 = 420.75/x
  3. Step 3: Cross multiply
    289.50x = 420.75 × 420.75
  4. Step 4: Simplify right side
    289.50x = 177,030.56
  5. Step 5: Solve for x
    x = 177,030.56/289.50
  6. Step 6: Final answer
    x = 611.50

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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.