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Finding the Third Proportional to 199 and 409.50

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Solution

The third proportional to 199 and 409.50 is: 842.66

Step by Step Solution

  1. Step 1: Write the proportion equation
    199 : 409.50 = 409.50 : x
  2. Step 2: Convert to fraction form
    199/409.50 = 409.50/x
  3. Step 3: Cross multiply
    199x = 409.50 × 409.50
  4. Step 4: Simplify right side
    199x = 167,690.25
  5. Step 5: Solve for x
    x = 167,690.25/199
  6. Step 6: Final answer
    x = 842.66

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Why These Related Problems?

These problems maintain the same ratio (2.06) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.