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Finding the Third Proportional to 209.75 and 345.75

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Solution

The third proportional to 209.75 and 345.75 is: 569.93

Step by Step Solution

  1. Step 1: Write the proportion equation
    209.75 : 345.75 = 345.75 : x
  2. Step 2: Convert to fraction form
    209.75/345.75 = 345.75/x
  3. Step 3: Cross multiply
    209.75x = 345.75 × 345.75
  4. Step 4: Simplify right side
    209.75x = 119,543.06
  5. Step 5: Solve for x
    x = 119,543.06/209.75
  6. Step 6: Final answer
    x = 569.93

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Why These Related Problems?

These problems maintain the same ratio (1.65) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.