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Finding the Third Proportional to 416 and 723

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Solution

The third proportional to 416 and 723 is: 1,256.56

Step by Step Solution

  1. Step 1: Write the proportion equation
    416 : 723 = 723 : x
  2. Step 2: Convert to fraction form
    416/723 = 723/x
  3. Step 3: Cross multiply
    416x = 723 × 723
  4. Step 4: Simplify right side
    416x = 522,729
  5. Step 5: Solve for x
    x = 522,729/416
  6. Step 6: Final answer
    x = 1,256.56

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Why These Related Problems?

These problems maintain the same ratio (1.74) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.