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Finding the Third Proportional to 243 and 409

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Solution

The third proportional to 243 and 409 is: 688.40

Step by Step Solution

  1. Step 1: Write the proportion equation
    243 : 409 = 409 : x
  2. Step 2: Convert to fraction form
    243/409 = 409/x
  3. Step 3: Cross multiply
    243x = 409 × 409
  4. Step 4: Simplify right side
    243x = 167,281
  5. Step 5: Solve for x
    x = 167,281/243
  6. Step 6: Final answer
    x = 688.40

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Why These Related Problems?

These problems maintain the same ratio (1.68) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.