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Finding the Third Proportional to 409.75 and 590.50

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Solution

The third proportional to 409.75 and 590.50 is: 850.98

Step by Step Solution

  1. Step 1: Write the proportion equation
    409.75 : 590.50 = 590.50 : x
  2. Step 2: Convert to fraction form
    409.75/590.50 = 590.50/x
  3. Step 3: Cross multiply
    409.75x = 590.50 × 590.50
  4. Step 4: Simplify right side
    409.75x = 348,690.25
  5. Step 5: Solve for x
    x = 348,690.25/409.75
  6. Step 6: Final answer
    x = 850.98

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Why These Related Problems?

These problems maintain the same ratio (1.44) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.