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Finding the Third Proportional to 209.75 and 342.75

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Solution

The third proportional to 209.75 and 342.75 is: 560.08

Step by Step Solution

  1. Step 1: Write the proportion equation
    209.75 : 342.75 = 342.75 : x
  2. Step 2: Convert to fraction form
    209.75/342.75 = 342.75/x
  3. Step 3: Cross multiply
    209.75x = 342.75 × 342.75
  4. Step 4: Simplify right side
    209.75x = 117,477.56
  5. Step 5: Solve for x
    x = 117,477.56/209.75
  6. Step 6: Final answer
    x = 560.08

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Why These Related Problems?

These problems maintain the same ratio (1.63) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.