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Finding the Third Proportional to 296 and 409

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Solution

The third proportional to 296 and 409 is: 565.14

Step by Step Solution

  1. Step 1: Write the proportion equation
    296 : 409 = 409 : x
  2. Step 2: Convert to fraction form
    296/409 = 409/x
  3. Step 3: Cross multiply
    296x = 409 × 409
  4. Step 4: Simplify right side
    296x = 167,281
  5. Step 5: Solve for x
    x = 167,281/296
  6. Step 6: Final answer
    x = 565.14

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Why These Related Problems?

These problems maintain the same ratio (1.38) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.