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Finding the Third Proportional to 405 and 689.50

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Solution

The third proportional to 405 and 689.50 is: 1,173.85

Step by Step Solution

  1. Step 1: Write the proportion equation
    405 : 689.50 = 689.50 : x
  2. Step 2: Convert to fraction form
    405/689.50 = 689.50/x
  3. Step 3: Cross multiply
    405x = 689.50 × 689.50
  4. Step 4: Simplify right side
    405x = 475,410.25
  5. Step 5: Solve for x
    x = 475,410.25/405
  6. Step 6: Final answer
    x = 1,173.85

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Why These Related Problems?

These problems maintain the same ratio (1.70) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.