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Finding the Third Proportional to 180 and 289.50

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Solution

The third proportional to 180 and 289.50 is: 465.61

Step by Step Solution

  1. Step 1: Write the proportion equation
    180 : 289.50 = 289.50 : x
  2. Step 2: Convert to fraction form
    180/289.50 = 289.50/x
  3. Step 3: Cross multiply
    180x = 289.50 × 289.50
  4. Step 4: Simplify right side
    180x = 83,810.25
  5. Step 5: Solve for x
    x = 83,810.25/180
  6. Step 6: Final answer
    x = 465.61

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Why These Related Problems?

These problems maintain the same ratio (1.61) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.