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Finding the Third Proportional to 189.75 and 406.50

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Solution

The third proportional to 189.75 and 406.50 is: 870.84

Step by Step Solution

  1. Step 1: Write the proportion equation
    189.75 : 406.50 = 406.50 : x
  2. Step 2: Convert to fraction form
    189.75/406.50 = 406.50/x
  3. Step 3: Cross multiply
    189.75x = 406.50 × 406.50
  4. Step 4: Simplify right side
    189.75x = 165,242.25
  5. Step 5: Solve for x
    x = 165,242.25/189.75
  6. Step 6: Final answer
    x = 870.84

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Why These Related Problems?

These problems maintain the same ratio (2.14) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.