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Finding the Third Proportional to 282,416 and 414,976

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Solution

The third proportional to 282,416 and 414,976 is: 609,756.81

Step by Step Solution

  1. Step 1: Write the proportion equation
    282,416 : 414,976 = 414,976 : x
  2. Step 2: Convert to fraction form
    282,416/414,976 = 414,976/x
  3. Step 3: Cross multiply
    282,416x = 414,976 × 414,976
  4. Step 4: Simplify right side
    282,416x = 172,205,080,576
  5. Step 5: Solve for x
    x = 172,205,080,576/282,416
  6. Step 6: Final answer
    x = 609,756.81

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Why These Related Problems?

These problems maintain the same ratio (1.47) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.