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Finding the Third Proportional to 416 and 565

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Solution

The third proportional to 416 and 565 is: 767.37

Step by Step Solution

  1. Step 1: Write the proportion equation
    416 : 565 = 565 : x
  2. Step 2: Convert to fraction form
    416/565 = 565/x
  3. Step 3: Cross multiply
    416x = 565 × 565
  4. Step 4: Simplify right side
    416x = 319,225
  5. Step 5: Solve for x
    x = 319,225/416
  6. Step 6: Final answer
    x = 767.37

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Why These Related Problems?

These problems maintain the same ratio (1.36) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.