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Finding the Third Proportional to 202 and 407.75

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Solution

The third proportional to 202 and 407.75 is: 823.07

Step by Step Solution

  1. Step 1: Write the proportion equation
    202 : 407.75 = 407.75 : x
  2. Step 2: Convert to fraction form
    202/407.75 = 407.75/x
  3. Step 3: Cross multiply
    202x = 407.75 × 407.75
  4. Step 4: Simplify right side
    202x = 166,260.06
  5. Step 5: Solve for x
    x = 166,260.06/202
  6. Step 6: Final answer
    x = 823.07

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Why These Related Problems?

These problems maintain the same ratio (2.02) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.