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Finding the Third Proportional to 205 and 293.50

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Solution

The third proportional to 205 and 293.50 is: 420.21

Step by Step Solution

  1. Step 1: Write the proportion equation
    205 : 293.50 = 293.50 : x
  2. Step 2: Convert to fraction form
    205/293.50 = 293.50/x
  3. Step 3: Cross multiply
    205x = 293.50 × 293.50
  4. Step 4: Simplify right side
    205x = 86,142.25
  5. Step 5: Solve for x
    x = 86,142.25/205
  6. Step 6: Final answer
    x = 420.21

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Why These Related Problems?

These problems maintain the same ratio (1.43) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.